A cluster Monte Carlo algorithm with a conserved order parameter

TL;DR

This paper introduces a cluster Monte Carlo algorithm for fixed order parameter ensembles, utilizing the tethered ensemble to accurately recover canonical averages and effectively study critical phenomena.

Contribution

The paper presents a novel cluster algorithm based on the tethered ensemble, enabling fixed order parameter simulations with accurate canonical averages and improved analysis of critical properties.

Findings

Critical slowing down comparable to canonical algorithms

Accurate recovery of canonical averages

Competitive estimation of the 3D Ising anomalous dimension

Abstract

We propose a cluster simulation algorithm for statistical ensembles with fixed order parameter. We use the tethered ensemble, which features Helmholtz's effective potential rather than Gibbs's free energy, and in which canonical averages are recovered with arbitrary accuracy. For the D = 2,3 Ising model our method's critical slowing down is comparable to that of canonical cluster algorithms. Yet, we can do more than merely reproduce canonical values. As an example, we obtain a competitive value for the 3D Ising anomalous dimension from the maxima of the effective potential.