Showing 1–5 of 5 results for author: Pei, Y R

At Most Two Infinite Blue Clusters in the CMR Representation of the Edwards-Anderson Spin Glass

Authors: Yan Ru Pei

Abstract: The two-replica Chayes-Machta-Redner (CMR) representation is one of the main proposed geometric signatures of spin-glass order in the short-range Edwards-Anderson model. Mean-field arguments and recent numerics suggest that the low-temperature phase should exhibit two macroscopic blue clusters carrying opposite overlap signs. We prove a rigorous structural constraint in this direction. For any sub… ▽ More The two-replica Chayes-Machta-Redner (CMR) representation is one of the main proposed geometric signatures of spin-glass order in the short-range Edwards-Anderson model. Mean-field arguments and recent numerics suggest that the low-temperature phase should exhibit two macroscopic blue clusters carrying opposite overlap signs. We prove a rigorous structural constraint in this direction. For any subsequential local weak limit of the standard periodic-torus joint laws on disorder, two spin replicas, and CMR bond variables, the blue subgraph contains at most two infinite connected components; if two exist, then they lie in a common infinite grey cluster and belong to opposite overlap-parity classes. The main obstacle is that the labelled blue geometry does not permit unrestricted insertions across overlap classes, and no positive-association input is available, so the usual Burton-Keane and random-cluster arguments do not apply directly. We isolate an abstract multicolour Burton-Keane proposition based on finite-box label-class coalescence and verify its hypothesis for CMR blue bonds by resampling the full joint measure. As auxiliary input, we establish finite energy and a percolation transition for the grey subgraph via local resampling of the disorder and a parity-based Peierls estimate. These results do not prove the existence of infinite blue clusters or a spin-glass phase transition, but they give a rigorous upper bound compatible with the two-cluster picture for short-range spin glasses. △ Less

Submitted 6 July, 2026; v1 submitted 17 May, 2026; originally announced May 2026.

Comments: 19 pages, 1 numbered figure and 1 unnumbered proof-dependency diagram

peapods: A Rust-Accelerated Monte Carlo Package for Ising Spin Systems

Authors: Yan Ru Pei

Abstract: We present peapods (github.com/PeaBrane/peapods), an open-source Python package for Monte Carlo simulation of Ising spin systems with arbitrary coupling constants on periodic Bravais lattices with user-specified neighbor offsets. The computational core is written in Rust and exposed to Python via PyO3, combining the ergonomic interface of Python with the performance of compiled, memory-safe code.… ▽ More We present peapods (github.com/PeaBrane/peapods), an open-source Python package for Monte Carlo simulation of Ising spin systems with arbitrary coupling constants on periodic Bravais lattices with user-specified neighbor offsets. The computational core is written in Rust and exposed to Python via PyO3, combining the ergonomic interface of Python with the performance of compiled, memory-safe code. The package implements Metropolis and Gibbs single-spin-flip algorithms, Swendsen-Wang and Wolff cluster updates, parallel tempering, and three replica cluster moves for spin glasses: the Houdayer isoenergetic cluster move, the Jorg stochastic variant, and the Chayes-Machta-Redner (CMR) blue-bond algorithm. Overlap statistics between replica pairs enable computation of the spin glass order parameter and Binder ratio. Replica-level parallelism is achieved through the Rayon work-stealing scheduler. We validate the implementation against the exact critical temperatures of the two-dimensional Ising model on the square and triangular lattices via finite-size scaling of the Binder cumulant. △ Less

Submitted 4 March, 2026; v1 submitted 21 February, 2026; originally announced February 2026.

A Finite-temperature Phase Transition for the Ising Spin-glass in $d\geq 2$

Authors: Yan Ru Pei, Massimiliano Di Ventra

Abstract: It is believed that the $\pm J$ Ising spin-glass does not order at finite temperatures in dimension $d=2$. However, using a graphical representation and a contour argument, we prove rigorously the existence of a finite-temperature phase transition in $d\geq 2$ with $T_c \geq 0.4$. In the graphical representation, the low-temperature phase allows for the coexistence of multiple infinite clusters ea… ▽ More It is believed that the $\pm J$ Ising spin-glass does not order at finite temperatures in dimension $d=2$. However, using a graphical representation and a contour argument, we prove rigorously the existence of a finite-temperature phase transition in $d\geq 2$ with $T_c \geq 0.4$. In the graphical representation, the low-temperature phase allows for the coexistence of multiple infinite clusters each with a rigidly aligned spin-overlap state. These clusters correlate negatively with each other, and are entropically stable without breaking any global symmetry. They can emerge in most graph structures and disorder measures. △ Less

Submitted 19 September, 2022; v1 submitted 3 May, 2021; originally announced May 2021.

Comments: The proof of the finitude of zero-energy contours in Appendix D.2 contains a technical error, where we failed to notice that opening a red bond in any of the four quadrants can possibly restrict opening of any blue bonds in the contour. This means that the probability that the contour is zero-energy (no blue-bonds) cannot be bounded exponentially, thus the result does not immediately follow

MSC Class: 05C22; 82B05

Non-equilibrium criticality and efficient exploration of glassy landscapes with memory dynamics

Authors: Yan Ru Pei, Massimiliano Di Ventra

Abstract: Spin glasses are notoriously difficult to study both analytically and numerically due to the presence of frustration and metastability. Their highly non-convex landscapes require collective updates to explore efficiently. Currently, most state-of-the-art algorithms rely on stochastic spin clusters to perform non-local updates, but such "cluster algorithms" lack general efficiency. Here, we introdu… ▽ More Spin glasses are notoriously difficult to study both analytically and numerically due to the presence of frustration and metastability. Their highly non-convex landscapes require collective updates to explore efficiently. Currently, most state-of-the-art algorithms rely on stochastic spin clusters to perform non-local updates, but such "cluster algorithms" lack general efficiency. Here, we introduce a non-equilibrium approach for simulating spin glasses based on classical dynamics with memory. By simulating various classes of 3d spin glasses (Edwards-Anderson, partially-frustrated, and fully-frustrated models), we find that memory dynamically promotes critical spin clusters during time evolution, in a self-organizing manner. This facilitates an efficient exploration of the low-temperature phases of spin glasses. △ Less

Submitted 27 March, 2021; v1 submitted 8 February, 2021; originally announced February 2021.

Comments: 21 pages, 9 figures

Efficient Solution of Boolean Satisfiability Problems with Digital MemComputing

Authors: S. R. B. Bearden, Y. R. Pei, M. Di Ventra

Abstract: Boolean satisfiability is a propositional logic problem of interest in multiple fields, e.g., physics, mathematics, and computer science. Beyond a field of research, instances of the SAT problem, as it is known, require efficient solution methods in a variety of applications. It is the decision problem of determining whether a Boolean formula has a satisfying assignment, believed to require expone… ▽ More Boolean satisfiability is a propositional logic problem of interest in multiple fields, e.g., physics, mathematics, and computer science. Beyond a field of research, instances of the SAT problem, as it is known, require efficient solution methods in a variety of applications. It is the decision problem of determining whether a Boolean formula has a satisfying assignment, believed to require exponentially growing time for an algorithm to solve for the worst-case instances. Yet, the efficient solution of many classes of Boolean formulae eludes even the most successful algorithms, not only for the worst-case scenarios, but also for typical-case instances. Here, we introduce a memory-assisted physical system (a digital memcomputing machine) that, when its non-linear ordinary differential equations are integrated numerically, shows evidence for polynomially-bounded scalability while solving "hard" planted-solution instances of SAT, known to require exponential time to solve in the typical case for both complete and incomplete algorithms. Furthermore, we analytically demonstrate that the physical system can efficiently solve the SAT problem in continuous time, without the need to introduce chaos or an exponentially growing energy. The efficiency of the simulations is related to the collective dynamical properties of the original physical system that persist in the numerical integration to robustly guide the solution search even in the presence of numerical errors. We anticipate our results to broaden research directions in physics-inspired computing paradigms ranging from theory to application, from simulation to hardware implementation. △ Less

Submitted 12 November, 2020; originally announced November 2020.

Journal ref: Scientific Reports 10, 19741 (2020)