A single-walker approach for studying quasi-ergodic systems

TL;DR

This paper revisits and updates the jump-walking Monte-Carlo algorithm to effectively study equilibrium properties of quasi-ergodic systems using a single processing thread, overcoming limitations of standard methods.

Contribution

The paper introduces an improved single-walker jump-walking algorithm for quasi-ergodic systems, enabling equilibrium analysis without parallel processing.

Findings

Successfully applied to Ising model and lattice-gas sorption in aerogel.

Produced equilibrium isotherms hidden by hysteresis in standard simulations.

Demonstrated effectiveness at low temperatures with slowed system dynamics.

Abstract

The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-ergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for large parallel processing systems. The updated algorithm is tested on the Ising model and applied to the lattice-gas model for sorption in aerogel at low temperatures, when dynamics of the system is critically slowed down. It is demonstrated that the updated jump-walking simulations are able to produce equilibrium isotherms which are typically hidden by the hysteresis effect characteristic of the standard single-flip simulations.