Equilibriumlike invaded cluster algorithm: critical exponents and dynamical properties

TL;DR

This paper introduces the Equilibriumlike invaded cluster (EIC) algorithm, an extension of the invaded cluster method, which accurately determines critical exponents and dynamical properties of the Potts model while maintaining equilibrium conditions.

Contribution

The paper presents the EIC algorithm that improves critical exponent estimation and explores its dynamical properties, extending the invaded cluster approach.

Findings

High-precision critical exponents for Potts model

Effective determination of thermal and magnetic exponents

Discussion of dynamical properties and Li-Sokal bound

Abstract

We present a detailed study of the Equilibriumlike invaded cluster algorithm (EIC), recently proposed as an extension of the invaded cluster (IC) algorithm, designed to drive the system to criticality while still preserving the equilibrium ensemble. We perform extensive simulations on two special cases of the Potts model and examine the precision of critical exponents by including the leading corrections. We show that both thermal and magnetic critical exponents can be obtained with high accuracy compared to the best available results. The choice of the auxiliary parameters of the algorithm is discussed in context of dynamical properties. We also discuss the relation to the Li-Sokal bound for the dynamical exponent $z$.