Transition path sampling algorithm for discrete many-body systems

TL;DR

This paper introduces a new Monte Carlo path-sampling algorithm for discrete many-body systems, enabling efficient transition rate calculations and scalable simulations, demonstrated on the 2D Ising model.

Contribution

A novel path-sampling Monte Carlo method for discrete systems that efficiently computes transition rates and scales well with system size.

Findings

Method agrees with existing results for the 2D Ising model.

Scales efficiently with system size, suitable for large systems.

Provides complementary insights compared to other algorithms.

Abstract

We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions, including systems that are out of equilibrium. We combine the proposed path-sampling algorithm with thermodynamic integration to calculate transition rates. We demonstrate our method on the well studied 2D Ising model with periodic boundary conditions, and show agreement with other results both for large and small system sizes. The method scales well with the system size, allowing one to simulate systems with many degrees of freedom, and providing complementary information with respect to other algorithms.