Probability distributions of the work in the 2D-Ising model

TL;DR

This paper uses Monte Carlo simulations to analyze the probability distributions of magnetic work in the 2D Ising model across different temperatures, applying the Jarzynski equality to compute free energy differences and examining critical behavior.

Contribution

It introduces a comprehensive simulation approach to study work distributions and free energy calculations in the 2D Ising model near criticality.

Findings

Work distributions vary with temperature and rate of field growth.

Free energy differences are accurately computed using Jarzynski equality.

Critical exponent δ is estimated from the data.

Abstract

Probability distributions of the magnetic work are computed for the 2D Ising model by means of Monte Carlo simulations. The system is first prepared at equilibrium for three temperatures below, at and above the critical point. A magnetic field is then applied and grown linearly at different rates. Probability distributions of the work are stored and free energy differences computed using the Jarzynski equality. Consistency is checked and the dynamics of the system is analyzed. Free energies and dissipated works are reproduced with simple models. The critical exponent $\delta$ is estimated in an usual manner.