Robust Parameter Selection for Parallel Tempering

TL;DR

This paper introduces an iterative algorithm for selecting optimal parameter values in Parallel Tempering Monte Carlo simulations, significantly improving equilibration especially in systems with first-order phase transitions.

Contribution

It presents a novel, iterative respacing method for parameter selection that enhances the efficiency of Parallel Tempering simulations for complex systems.

Findings

Improved equilibration in Ising spin systems with first-order phase transitions.

Effective parameter selection method demonstrated on Quantum Monte Carlo systems.

Iterative respacing leads to better simulation performance.

Abstract

This paper describes an algorithm for selecting parameter values (e.g. temperature values) at which to measure equilibrium properties with Parallel Tempering Monte Carlo simulation. Simple approaches to choosing parameter values can lead to poor equilibration of the simulation, especially for Ising spin systems that undergo $1^st$-order phase transitions. However, starting from an initial set of parameter values, the careful, iterative respacing of these values based on results with the previous set of values greatly improves equilibration. Example spin systems presented here appear in the context of Quantum Monte Carlo.