Tethered Monte Carlo: Managing rugged free-energy landscapes with a Helmholtz-potential formalism

TL;DR

This paper introduces the Tethered Monte Carlo method, which uses a Helmholtz-potential formalism to efficiently explore rugged free-energy landscapes, demonstrated through applications in crystallization and magnetic phase transitions.

Contribution

The paper presents a novel tethered Monte Carlo approach that accurately computes Helmholtz free energies and reduces dynamic slowing-down in simulations of complex systems.

Findings

Successfully applied to hard spheres crystallization

Effective in studying phase transitions in disordered magnetic systems

Reduces algorithmic slowing-down in Monte Carlo simulations

Abstract

Tethering methods allow us to perform Monte Carlo simulations in ensembles with conserved quantities. Specifically, one couples a reservoir to the physical magnitude of interest, and studies the statistical ensemble where the total magnitude (system+reservoir) is conserved. The reservoir is actually integrated out, which leaves us with a fluctuation-dissipation formalism that allows us to recover the appropriate Helmholtz effective potential with great accuracy. These methods are demonstrating a remarkable flexibility. In fact, we illustrate two very different applications: hard spheres crystallization and the phase transition of the diluted antiferromagnet in a field (the physical realization of the random field Ising model). The tethered approach holds the promise to transform cartoon drawings of corrugated free-energy landscapes into real computations. Besides, it reduces the algorithmic dynamic slowing-down, probably because the conservation law holds non-locally.