Exploring Replica-Exchange Wang-Landau sampling in higher-dimensional parameter space

TL;DR

This paper extends the replica-exchange Wang-Landau algorithm to higher-dimensional parameter spaces, enabling efficient and ergodic sampling of complex systems like the 2D Ising model, overcoming previous discontinuity issues.

Contribution

It introduces a higher-dimensional hybrid replica-exchange Wang-Landau scheme that improves sampling efficiency and continuity in the density of states across parameter spaces.

Findings

Successfully applied to the 2D Ising model

Overcomes discontinuities in density of states

Scales efficiently with many computing cores

Abstract

We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of Wang-Landau and Replica-Exchange algorithms, and the one-dimensional version of this approach has been shown to be very efficient and to scale well, up to several thousands of computing cores. This approach allows us to split the parameter space of the system to be simulated into several pieces and still perform a random walk over the entire parameter range, ensuring the ergodicity of the simulation. Previous work, in which a similar scheme of parallel simulation was implemented without using replica exchange and with a different way to combine the result from the pieces, led to discontinuities in the final density of states over the entire range of parameters. From our simulations, it appears that the replica-exchange Wang-Landau algorithm is able to overcome this difficulty, allowing exploration of higher parameter phase space by keeping track of the joint density of states.