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Roadmap on Advancements of the FHI-aims Software Package
Authors:
Joseph W. Abbott,
Carlos Mera Acosta,
Alaa Akkoush,
Alberto Ambrosetti,
Viktor Atalla,
Alexej Bagrets,
Jörg Behler,
Daniel Berger,
Hannah Bertschi,
Björn Bieniek,
Jonas Björk,
Volker Blum,
Saeed Bohloul,
Connor L. Box,
Nicholas Boyer,
Danilo Simoes Brambila,
Gabriel A. Bramley,
Kyle R. Bryenton,
María Camarasa-Gómez,
Christian Carbogno,
Fabio Caruso,
Sucismita Chutia,
Michele Ceriotti,
Gábor Csányi,
William Dawson
, et al. (181 additional authors not shown)
Abstract:
Electronic-structure theory is the foundation of the description of materials including multiscale modeling of their properties and functions. Obviously, without sufficient accuracy at the base, reliable predictions are unlikely at any level that follows. The software package FHI-aims has proven to be a game changer for accurate free-energy calculations because of its scalability, numerical precis…
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Electronic-structure theory is the foundation of the description of materials including multiscale modeling of their properties and functions. Obviously, without sufficient accuracy at the base, reliable predictions are unlikely at any level that follows. The software package FHI-aims has proven to be a game changer for accurate free-energy calculations because of its scalability, numerical precision, and its efficient handling of density functional theory (DFT) with hybrid functionals and van der Waals interactions. It treats molecules, clusters, and extended systems (solids and liquids) on an equal footing. Besides DFT, FHI-aims also includes quantum-chemistry methods, descriptions for excited states and vibrations, and calculations of various types of transport. Recent advancements address the integration of FHI-aims into an increasing number of workflows and various artificial intelligence (AI) methods. This Roadmap describes the state-of-the-art of FHI-aims and advancements that are currently ongoing or planned.
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Submitted 20 April, 2026; v1 submitted 30 April, 2025;
originally announced May 2025.
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Multipartite entanglement in a Josephson Junction Laser
Authors:
Ben Lang,
Andrew D. Armour
Abstract:
We analyse the entanglement in a model Josephson photonics system in which a dc voltage-biased Josephson junction couples a collection of cavity modes and populates them with microwave photons. Using an approximate quadratic Hamiltonian model, we study the Gaussian entanglement that develops between the modes as the Josephson energy of the system is increased. We find that the modes in the system…
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We analyse the entanglement in a model Josephson photonics system in which a dc voltage-biased Josephson junction couples a collection of cavity modes and populates them with microwave photons. Using an approximate quadratic Hamiltonian model, we study the Gaussian entanglement that develops between the modes as the Josephson energy of the system is increased. We find that the modes in the system fall into a series of blocks, with bipartite entanglement generated between modes within a given block. Tripartite entanglement between modes within a given block is also widespread, though it is limited to certain ranges of the Josephson energy. The system could provide an alternative route to generating multimode microwave entanglement, an important resource in quantum technologies, without the need for ac excitation.
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Submitted 1 October, 2024;
originally announced October 2024.
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Discrete time translation symmetry breaking in a Josephson junction laser
Authors:
Ben Lang,
Grace F. Morley,
Andrew D. Armour
Abstract:
A Josephson junction laser is realised when a microwave cavity is driven by a voltage-biased Josephson junction. Through the ac Josephson effect, a dc voltage generates a periodic drive that acts on the cavity and generates interactions between its modes. A sufficiently strong drive enables processes that down-convert a drive resonant with a high harmonic into photons at the cavity fundamental fre…
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A Josephson junction laser is realised when a microwave cavity is driven by a voltage-biased Josephson junction. Through the ac Josephson effect, a dc voltage generates a periodic drive that acts on the cavity and generates interactions between its modes. A sufficiently strong drive enables processes that down-convert a drive resonant with a high harmonic into photons at the cavity fundamental frequency, breaking the discrete time translation symmetry set by the Josephson frequency. Using a classical model, we determine when and how this transition occurs as a function of the bias voltage and the number of cavity modes. We find that certain combinations of mode number and voltage tend to facilitate the transition which emerges via an instability within a subset of the modes. Despite the complexity of the system, there are cases in which the critical drive strength can be obtained analytically.
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Submitted 5 August, 2022;
originally announced August 2022.
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Josephson Photonics with Simultaneous Resonances
Authors:
Kieran Wood,
Andrew D. Armour,
Ben Lang
Abstract:
Inelastic Cooper pair tunneling across a voltage-biased Josephson junction in series with one or more microwave cavities can generate photons via resonant processes in which the energy lost by the Cooper pair matches that of the photon(s) produced. We generalise previous theoretical treatments of such systems to analyse cases where two or more different photon generation processes are resonant sim…
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Inelastic Cooper pair tunneling across a voltage-biased Josephson junction in series with one or more microwave cavities can generate photons via resonant processes in which the energy lost by the Cooper pair matches that of the photon(s) produced. We generalise previous theoretical treatments of such systems to analyse cases where two or more different photon generation processes are resonant simultaneously. We also explore in detail a specific case where generation of a single photon in one cavity mode is simultaneously resonant with the generation of two photons in a second mode. We find that the coexistence of the two resonances leads to effective couplings between the modes which in turn generate entanglement.
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Submitted 4 October, 2021; v1 submitted 29 June, 2021;
originally announced June 2021.
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Quartic multifractality and finite-size corrections at the spin quantum Hall transition
Authors:
Martin Puschmann,
Daniel Hernangómez-Pérez,
Bruno Lang,
Soumya Bera,
Ferdinand Evers
Abstract:
The spin quantum Hall (or class C) transition represents one of the few localization-delocalization transitions for which some of the critical exponents are known exactly. Not known, however, is the multifractal spectrum, $τ_q$, which describes the system-size scaling of inverse participation ratios $P_q$, i.e., the $q$-moments of critical wavefunction amplitudes. We here report simulations based…
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The spin quantum Hall (or class C) transition represents one of the few localization-delocalization transitions for which some of the critical exponents are known exactly. Not known, however, is the multifractal spectrum, $τ_q$, which describes the system-size scaling of inverse participation ratios $P_q$, i.e., the $q$-moments of critical wavefunction amplitudes. We here report simulations based on the class C Chalker-Coddington network and demonstrate that $τ_q$ is (essentially) a quartic polynomial in $q$. Analytical results fix all prefactors except the quartic curvature that we obtain as $γ=(2.22\pm{0.15})\cdot10^{-3}$. In order to achieve the necessary accuracy in the presence of sizable corrections to scaling, we have analyzed the evolution with system size of the entire $P_q$-distribution function. As it turns out, in a sizable window of $q$-values this distribution function exhibits a (single-parameter) scaling collapse already in the pre-asymptotic regime, where finite-size corrections are not negligible. This observation motivates us to propose a novel approach for extracting $τ_q$ based on concepts borrowed from the Kolmogorov-Smirnov test of mathematical statistics. We believe that our work provides the conceptual means for high-precision investigations of multifractal spectra also near other localization-delocalization transitions of current interest, especially the integer (class A) quantum Hall effect.
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Submitted 7 July, 2021; v1 submitted 25 April, 2021;
originally announced April 2021.
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Multi-Photon Resonances in Josephson Junction-Cavity Circuits
Authors:
Ben Lang,
Andrew D. Armour
Abstract:
We explore the dissipative dynamics of nonlinearly driven oscillator systems tuned to resonances where multiple excitations are generated. Such systems are readily realised in circuit QED systems combining Josephson junctions with a microwave cavity and a drive achieved either through flux or voltage bias. For resonances involving 3 or more photons the system undergoes a sequence of two closely sp…
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We explore the dissipative dynamics of nonlinearly driven oscillator systems tuned to resonances where multiple excitations are generated. Such systems are readily realised in circuit QED systems combining Josephson junctions with a microwave cavity and a drive achieved either through flux or voltage bias. For resonances involving 3 or more photons the system undergoes a sequence of two closely spaced dynamical transitions (the first one discontinuous and the second continuous) as the driving is increased leading to steady states that form complex periodic structures in phase space. In the vicinity of the transitions the system displays interesting bistable behaviour: we find that coherent effects can lead to surprising oscillations in the weight of the different dynamical states in the steady state of the system with increasing drive. We show that the dynamics is well-described by a simple effective rate model with transitions between states localised at different points in the phase space crystal. The oscillations in the weights of the dynamical states is reflected in corresponding oscillations in a time-scale that describes transitions between the states.
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Submitted 18 December, 2020;
originally announced December 2020.
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Collectively enhanced chiral photon emission from an atomic array near a nanofiber
Authors:
Ryan Jones,
Giuseppe Buonaiuto,
Ben Lang,
Igor Lesanovsky,
Beatriz Olmos
Abstract:
Emitter ensembles interact collectively with the radiation field. In the case of a one-dimensional array of atoms near a nanofiber, this collective light-matter interaction does not only lead to an increased photon coupling to the guided modes within the fiber, but also to a drastic enhancement of the chirality in the photon emission. We show that near-perfect chirality is already achieved for mod…
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Emitter ensembles interact collectively with the radiation field. In the case of a one-dimensional array of atoms near a nanofiber, this collective light-matter interaction does not only lead to an increased photon coupling to the guided modes within the fiber, but also to a drastic enhancement of the chirality in the photon emission. We show that near-perfect chirality is already achieved for moderately-sized ensembles, containing 10 to 15 atoms. This is of importance for developing an efficient interface between atoms and waveguide structures with unidirectional coupling, with applications in quantum computing and communication such as the development of non-reciprocal photon devices or quantum information transfer channels.
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Submitted 4 October, 2019;
originally announced October 2019.
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99% beta factor and directional coupling of quantum dots to fast light in photonic crystal waveguides determined by hyperspectral imaging
Authors:
L. Scarpelli,
B. Lang,
F. Masia,
D. M. Beggs,
E. A. Muljarov,
A. B. Young,
R. Oulton,
M. Kamp,
S. Höfling,
C. Schneider,
W. Langbein
Abstract:
Spontaneous emission from excitonic transitions in InAs/GaAs quantum dots embedded in photonic crystal waveguides at 5K into non-guided and guided modes is determined by direct hyperspectral imaging. This enables measurement of the absolute coupling efficiency into the guided modes, the beta-factor, directly, without assumptions on decay rates used previously. Notably, we found beta-factors above…
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Spontaneous emission from excitonic transitions in InAs/GaAs quantum dots embedded in photonic crystal waveguides at 5K into non-guided and guided modes is determined by direct hyperspectral imaging. This enables measurement of the absolute coupling efficiency into the guided modes, the beta-factor, directly, without assumptions on decay rates used previously. Notably, we found beta-factors above 90% over a wide spectral range of 40meV in the fast light regime, reaching a maximum of (99 $\pm$ 1)%. We measure the directional emission of the circularly polarized transitions in a magnetic field into counter-propagating guided modes, to deduce the mode circularity at the quantum dot sites. We find that points of high directionality, up to 97%, correlate with a reduced beta-factor, consistent with their positions away from the mode field antinode. By comparison with calibrated finite-difference time-domain simulations, we use the emission energy, mode circularity and beta-factor to estimate the quantum dot position inside the photonic crystal waveguide unit cell.
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Submitted 3 May, 2019;
originally announced May 2019.
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Self-consistent-field ensembles of disordered Hamiltonians: Efficient solver and application to superconducting films
Authors:
Matthias Stosiek,
Bruno Lang,
Ferdinand Evers
Abstract:
Our general interest is in self-consistent-field (scf) theories of disordered fermions. They generate physically relevant sub-ensembles ("scf-ensembles") within a given Altland-Zirnbauer class. We are motivated to investigate such ensembles (i) by the possibility to discover new fixed points due to (long-range) interactions; (ii) by analytical scf-theories that rely on partial self-consistency app…
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Our general interest is in self-consistent-field (scf) theories of disordered fermions. They generate physically relevant sub-ensembles ("scf-ensembles") within a given Altland-Zirnbauer class. We are motivated to investigate such ensembles (i) by the possibility to discover new fixed points due to (long-range) interactions; (ii) by analytical scf-theories that rely on partial self-consistency approximations awaiting a numerical validation; (iii) by the overall importance of scf-theories for the understanding of complex interaction-mediated phenomena in terms of effective single-particle pictures. In this paper we present an efficient, parallelized implementation solving scf-problems with spatially local fields by applying a kernel-polynomial approach. Our first application is the Boguliubov-deGennes (BdG) theory of the attractive-$U$ Hubbard model in the presence of on-site disorder; the scf-fields are the particle density $n(\mathbf{r})$ and the gap function $Δ(\mathbf{r})$. For this case, we reach system sizes unprecedented in earlier work. They allow us to study phenomena emerging at scales substantially larger than the lattice constant, such as the interplay of multifractality and interactions, or the formation of superconducting islands. For example, we observe that the coherence length exhibits a non-monotonic behavior with increasing disorder strength already at moderate $U$. With respect to methodology our results are important because we establish that partial self-consistency ("energy-only") schemes as typically employed in analytical approaches tend to miss qualitative physics such as island formation.
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Submitted 26 September, 2019; v1 submitted 25 March, 2019;
originally announced March 2019.
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Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects
Authors:
Andreas Alvermann,
Achim Basermann,
Hans-Joachim Bungartz,
Christian Carbogno,
Dominik Ernst,
Holger Fehske,
Yasunori Futamura,
Martin Galgon,
Georg Hager,
Sarah Huber,
Thomas Huckle,
Akihiro Ida,
Akira Imakura,
Masatoshi Kawai,
Simone Köcher,
Moritz Kreutzer,
Pavel Kus,
Bruno Lang,
Hermann Lederer,
Valeriy Manin,
Andreas Marek,
Kengo Nakajima,
Lydia Nemec,
Karsten Reuter,
Michael Rippl
, et al. (8 additional authors not shown)
Abstract:
We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highl…
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We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained.
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Submitted 4 June, 2018;
originally announced June 2018.
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High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations
Authors:
Andreas Pieper,
Moritz Kreutzer,
Andreas Alvermann,
Martin Galgon,
Holger Fehske,
Georg Hager,
Bruno Lang,
Gerhard Wellein
Abstract:
We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diag…
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We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need for matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the $10^2$ innermost eigenpairs of a topological insulator matrix with dimension $10^9$ derived from quantum physics applications.
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Submitted 10 May, 2016; v1 submitted 16 October, 2015;
originally announced October 2015.
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Signatures of Random Matrix Theory in the Discrete Energy Spectra of Subnanosize Metallic Clusters
Authors:
L. L. A. Adams,
B. W. Lang,
Yu Chen,
A. M. Goldman
Abstract:
Lead clusters deposited on Si(111) substrates have been studied at low temperatures using scanning tunneling microscopy and spectroscopy. The current-voltage characteristics exhibit current peaks that are irregularly spaced and varied in height. The statistics of the distribution of peak heights and spacings are in agreement with random matrix theory for several clusters. The distributions have…
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Lead clusters deposited on Si(111) substrates have been studied at low temperatures using scanning tunneling microscopy and spectroscopy. The current-voltage characteristics exhibit current peaks that are irregularly spaced and varied in height. The statistics of the distribution of peak heights and spacings are in agreement with random matrix theory for several clusters. The distributions have also been studied as a function of cluster shape.
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Submitted 1 May, 2007;
originally announced May 2007.
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Pinning frequencies of the collective modes in $α$-uranium
Authors:
B. Mihaila,
C. P. Opeil,
F. R. Drymiotis,
J. L. Smith,
J. C. Cooley,
M. E. Manley,
A. Migliori,
C. Mielke,
T. Lookman,
A. Saxena,
A. R. Bishop,
K. B. Blagoev,
D. J. Thoma,
B. E. Lang,
J. Boerio-Goates,
B. F. Woodfield,
G. M. Schmiedeshoff,
J. C. Lashley
Abstract:
Uranium is the only known element that features a charge-density wave (CDW) and superconductivity. We report a comparison of the specific heat of single-crystal and polycrystalline $α$-uranium. \red{Away from the the phase transition the specific heat of the polycrystal is larger than that of the single crystal, and the aim of this paper is to explain this difference.} In the single crystal we f…
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Uranium is the only known element that features a charge-density wave (CDW) and superconductivity. We report a comparison of the specific heat of single-crystal and polycrystalline $α$-uranium. \red{Away from the the phase transition the specific heat of the polycrystal is larger than that of the single crystal, and the aim of this paper is to explain this difference.} In the single crystal we find excess contributions to the heat capacity at 41 K, 38 K, and 23 K, with a Debye temperature, $Θ_D$ = 256 K. In the polycrystalline sample the heat capacity curve is thermally broadened ($Θ_D$ = 184 K), but no excess heat capacity was observed. The excess heat capacity, $C_φ$ (taken as the difference between the single crystal and polycrystal heat capacities) is well described in terms of collective-mode excitations above their respective pinning frequencies. This attribution is represented by a modified Debye spectrum with two cutoff frequencies, a pinning frequency, $ν_o$, for the pinned CDW (due to grain boundaries in the polycrystal), and a normal Debye acoustic frequency occurring in the single crystal. We explain the 50-year-old difference in Debye temperatures between heat capacity and ultrasonic measurements.
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Submitted 22 January, 2006;
originally announced January 2006.
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Observation of discrete energy levels in a quantum confined system
Authors:
L. L. A. Adams,
B. W. Lang,
A. M. Goldman
Abstract:
Low temperature scanning tunneling microscope images and spectroscopic data have been obtained on subnanometer size Pb clusters fabricated using the technique of buffer layer assisted growth. Discrete energy levels were resolved in current-voltage characteristics as current peaks rather than current steps. Distributions of peak voltage spacings and peak current heights were consistent with Wigne…
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Low temperature scanning tunneling microscope images and spectroscopic data have been obtained on subnanometer size Pb clusters fabricated using the technique of buffer layer assisted growth. Discrete energy levels were resolved in current-voltage characteristics as current peaks rather than current steps. Distributions of peak voltage spacings and peak current heights were consistent with Wigner-Dyson and Porter-Thomas distributions respectively, suggesting the relevance of random matrix theory to the description of the electronic eigenstates of the clusters. The observation of peaks rather than steps in the current-voltage characteristics is attributed to a resonant tunneling process involving the discrete energy levels of the cluster, the tip, and the states at the interface between the cluster and the substrate surface.
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Submitted 23 February, 2005;
originally announced February 2005.
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Numerical Extraction of Distributions of Space-charge and Polarization from Laser Intensity Modulation Method
Authors:
Enis Tuncer,
Sidney B. Lang
Abstract:
The Fredholm integral equation of the laser intensity modulation method is solved with the application of the Monte Carlo technique and a least-squares solver. The numerical procedure is tested on simulated data.
The Fredholm integral equation of the laser intensity modulation method is solved with the application of the Monte Carlo technique and a least-squares solver. The numerical procedure is tested on simulated data.
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Submitted 8 September, 2004;
originally announced September 2004.
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The zeros of the QCD partition function
Authors:
A. D. Jackson,
C. B. Lang,
M. Oswald,
K. Splittorff
Abstract:
We establish a relationship between the zeros of the partition function in the complex mass plane and the spectral properties of the Dirac operator in QCD. This relation is derived within the context of chiral Random Matrix Theory and applies to QCD when chiral symmetry is spontaneously broken. Further, we introduce and examine the concept of normal modes in chiral spectra. Using this formalism…
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We establish a relationship between the zeros of the partition function in the complex mass plane and the spectral properties of the Dirac operator in QCD. This relation is derived within the context of chiral Random Matrix Theory and applies to QCD when chiral symmetry is spontaneously broken. Further, we introduce and examine the concept of normal modes in chiral spectra. Using this formalism we study the consequences of a finite Thouless energy for the zeros of the partition function. This leads to the demonstration that certain features of the QCD partition function are universal.
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Submitted 20 August, 2001;
originally announced August 2001.
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Elastic and thermodynamic properties of the shape-memory alloy AuZn
Authors:
T. W. Darling,
F. Chu,
A. Migliori,
D. J. thoma,
J. C. Lashley,
B. E. Lang,
J. Boerio-Goates,
B. F. Woodfield
Abstract:
The current work reports on the elastic shear moduli, internal friction, and the specific heat of the B2 cubic ordered alloy AuZn as a function of temperature. Measurements were made on single-crystal and polycrystalline samples using Resonant Ultrasound Spectroscopy (RUS), semi-adiabatic calorimetry and stress-strain measurements. Our results confirm that this alloy exhibits the shape-memory ef…
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The current work reports on the elastic shear moduli, internal friction, and the specific heat of the B2 cubic ordered alloy AuZn as a function of temperature. Measurements were made on single-crystal and polycrystalline samples using Resonant Ultrasound Spectroscopy (RUS), semi-adiabatic calorimetry and stress-strain measurements. Our results confirm that this alloy exhibits the shape-memory effect and a phase transition at 64.75 K that appears to be continuous (second-order) from the specific heat data. It is argued that the combination of equiatomic composition and a low transformation temperature constrain the chemical potential and its derivatives to exhibit behavior that lies at the borderline between that of a first-order (discontinuous) and a continuous phase transition. The acoustic dissipation does not peak at the transtion temperature as expected, but shows a maximum well into the low-temperature phase. The Debye temeprature value of 219 K, obtained from the low-temperature specific heat data is in favorable agreement with that determined from the acoustic data (207 K) above the transition.
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Submitted 9 August, 2001;
originally announced August 2001.
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Universality of the Ising Model on Sphere-like Lattices
Authors:
Ch. Hoelbling,
C. B. Lang
Abstract:
We study the 2D Ising model on three different types of lattices that are topologically equivalent to spheres. The geometrical shapes are reminiscent of the surface of a pillow, a 3D cube and a sphere, respectively. Systems of volumes ranging up to O($10^5$) sites are simulated and finite size scaling is analyzed. The partition function zeros and the values of various cumulants at their respecti…
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We study the 2D Ising model on three different types of lattices that are topologically equivalent to spheres. The geometrical shapes are reminiscent of the surface of a pillow, a 3D cube and a sphere, respectively. Systems of volumes ranging up to O($10^5$) sites are simulated and finite size scaling is analyzed. The partition function zeros and the values of various cumulants at their respective peak positions are determined and they agree with the scaling behavior expected from universality with the Onsager solution on the torus ($ν=1$). For the pseudocritical values of the coupling we find significant anomalies indicating a shift exponent $\neq 1$ for sphere-like lattice topology.
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Submitted 26 February, 1996;
originally announced February 1996.
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Strong Coupling Lattice Schwinger Model on Large Spherelike Lattices
Authors:
H. Gausterer,
C. B. Lang
Abstract:
The lattice regularized Schwinger model for one fermion flavor and in the strong coupling limit is studied through its equivalent representation as a restricted 8-vertex model. The Monte Carlo simulation on lattices with torus-topology is handicapped by a severe non-ergodicity of the updating algorithm; introducing lattices with spherelike topology avoids this problem. We present a large scale s…
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The lattice regularized Schwinger model for one fermion flavor and in the strong coupling limit is studied through its equivalent representation as a restricted 8-vertex model. The Monte Carlo simulation on lattices with torus-topology is handicapped by a severe non-ergodicity of the updating algorithm; introducing lattices with spherelike topology avoids this problem. We present a large scale study leading to the identification of a critical point with critical exponent $ν=1$, in the universality class of the Ising model or, equivalently, the lattice model of free fermions.
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Submitted 27 June, 1995;
originally announced June 1995.