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

TL;DR

peapods is an open-source Python package for Monte Carlo simulations of Ising spin systems, combining Rust's performance with Python's usability, supporting various algorithms and enabling advanced spin glass analysis.

Contribution

The package integrates Rust and Python to provide high-performance, versatile Monte Carlo simulation tools for Ising models with complex interactions.

Findings

Validated against exact critical temperatures of 2D Ising models

Supports multiple algorithms including cluster updates and parallel tempering

Enables detailed spin glass analysis with replica overlap statistics

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. 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.