Three-dimensional Ising model in the fixed-magnetization ensemble: a Monte Carlo study

TL;DR

This study uses a geometric cluster Monte Carlo algorithm to analyze the three-dimensional Ising model at criticality in the fixed-magnetization ensemble, revealing finite-size effects and connections to the canonical ensemble.

Contribution

It introduces a new approach to study the 3D Ising model at criticality in the fixed-magnetization ensemble using geometric cluster Monte Carlo methods.

Findings

Established a relation between the fixed-magnetization ensemble and the canonical ensemble.

Analyzed finite-size effects on the magnetization and magnetic field relation.

Connected microscopic spin probabilities to macroscopic thermodynamic quantities.

Abstract

We study the three-dimensional Ising model at the critical point in the fixed-magnetization ensemble, by means of the recently developed geometric cluster Monte Carlo algorithm. We define a magnetic-field-like quantity in terms of microscopic spin-up and spin-down probabilities in a given configuration of neighbors. In the thermodynamic limit, the relation between this field and the magnetization reduces to the canonical relation M(h). However, for finite systems, the relation is different. We establish a close connection between this relation and the probability distribution of the magnetization of a finite-size system in the canonical ensemble.