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

Alexandra Valentim,Julio C S Rocha,Shan-Ho Tsai,Markus Eisenbach,David P Landau,Carlos E Fiore,Ying Wai Li

doi:10.1088/1742-6596/640/1/012006

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.

Highlights

The Wang-Landau (WL) Monte Carlo method [1] is a sampling technique that can be used to obtain the density of states (DOS) of a system
It has the property of generating a flat histogram in some random walk space, where the parameters for the random walk and the flatness criterion can be chosen according to the system of interest [2, 3]
It would be of great interest to extend the one-dimensional replica exchange Wang-Landau (REWL) method [8, 9, 10] to a higher-dimensional parameter space, and implement a similar method that combines enhanced sampling techniques [12, 13, 17] and the advantages of parallel computing to obtain a joint density of states

Summary

Introduction

The Wang-Landau (WL) Monte Carlo method [1] is a sampling technique that can be used to obtain the density of states (DOS) of a system. 1. Introduction The Wang-Landau (WL) Monte Carlo method [1] is a sampling technique that can be used to obtain the density of states (DOS) of a system. It would be of great interest to extend the one-dimensional REWL method [8, 9, 10] to a higher-dimensional parameter space, and implement a similar method that combines enhanced sampling techniques [12, 13, 17] and the advantages of parallel computing to obtain a joint density of states.

Results

Conclusion