Reweighting for Nonequilibrium Markov Processes Using Sequential Importance Sampling Methods

TL;DR

This paper introduces a reweighting technique for nonequilibrium Markov processes that enables the calculation of physical quantities at various temperatures from a single simulation, enhancing efficiency in studying phase transitions.

Contribution

The authors develop a general reweighting method applicable to nonequilibrium Markov processes, allowing for temperature extrapolation from a single Monte Carlo simulation.

Findings

Efficiently computes temperature-dependent quantities from one simulation.

Applies to various systems and Monte Carlo schemes.

Demonstrates effectiveness with the Ising model.

Abstract

We present a generic reweighting method for nonequilibrium Markov processes. With nonequilibrium Monte Carlo simulations at a single temperature, one calculates the time evolution of physical quantities at different temperatures, which greatly saves the computational time. Using the dynamical finite-size scaling analysis for the nonequilibrium relaxation, one can study the dynamical properties of phase transitions together with the equilibrium ones. We demonstrate the procedure for the Ising model with the Metropolis algorithm, but the present formalism is general and can be applied to a variety of systems as well as with different Monte Carlo update schemes.