Local and cluster critical dynamics of the 3d random-site Ising model

TL;DR

This study uses Monte Carlo simulations to analyze how different algorithms affect the critical dynamics of a diluted 3D Ising model, revealing that dilution reduces the dynamical critical exponent for cluster algorithms.

Contribution

It provides the first detailed comparison of local and cluster algorithm dynamics in a diluted 3D Ising model, highlighting the impact of site dilution on critical slowing down.

Findings

Cluster algorithms have lower dynamical critical exponents than local algorithms.

Dilution decreases the dynamical critical exponent for cluster algorithms.

Dilution enhances critical slowing down in local dynamics.

Abstract

We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the Swendsen-Wang and Wolff cluster algorithms. The lattice sizes of L=10-96 are analysed by a finite-size-scaling technique. The site dilution concentration p=0.85 was chosen to minimize the correction-to-scaling effects. We calculate numerical values of the dynamical critical exponents for the integrated and exponential autocorrelation times for energy and magnetization. As expected, cluster algorithms are characterized by lower values of dynamical critical exponent than the local one: also in the case of dilution critical slowing down is more pronounced for the Metropolis algorithm. However, the striking feature of our estimates is that they suggest that dilution leads to decrease of the dynamical critical exponent for the cluster algorithms. This phenomenon is quite opposite to the local dynamics, where dilution enhances critical slowing down.