Spectral properties and lattice-size dependences in cluster algorithms

TL;DR

This paper analyzes the spectral properties and lattice-size dependence in cluster algorithms applied to Ising systems, providing insights into autocorrelation times, eigenvalues, and non-detailed balance observables across various dimensions.

Contribution

It offers a detailed analysis of spectral properties and lattice-size effects in cluster algorithms, including fit results for power-law behaviors and explanations for non-detailed balance observables.

Findings

Autocorrelation times depend on lattice size with power-law fits.

Eigenvalue weights exhibit specific lattice-size dependencies.

Behavior of non-detailed balance observables is explained through spectral analysis.

Abstract

Simulation results of Ising systems for several update rules, observables, and dimensions are analyzed. The lattice-size dependence is discussed for the autocorrelation times and for the weights of eigenvalues, giving fit results in the case of power laws. Implications of spectral properties are pointed out and the behavior of a particular observable not governed by detailed balance is explained.