Nonequilibrium free energy methods applied to magnetic systems: the degenerate Ising model

TL;DR

This paper reviews nonequilibrium Monte Carlo techniques for calculating free energies in magnetic systems and demonstrates their effectiveness by determining the phase diagram of the degenerate Ising model, aligning well with analytical results.

Contribution

It introduces and applies nonequilibrium free energy calculation methods to magnetic systems, specifically the degenerate Ising model, showing their accuracy and usefulness.

Findings

Good agreement with analytical phase diagrams

Effective calculation of free energy differences

Applicable to various magnetic models

Abstract

In this paper, we review the physical concepts of the nonequilibrium techniques for the calculation of free energies applied to magnetic systems using Monte Carlo simulations of different nonequilibrium processes. The methodology allows the calculation of the free energy difference between two different system Hamiltonians, as well as the free energy dependence on temperature and magnetic field for a given Hamiltonian. As an illustration of the effectiveness of this approach, we apply the methodologies to determine the phase diagram of a simple microscopic model, the degenerate Ising model. Our results show very good agreement with those obtained from analytical (theoretical) methods.