Stability of universal properties against perturbations of the Markov Chain Monte Carlo algorithm

TL;DR

This study demonstrates that universal properties at continuous phase transitions are remarkably stable against various perturbations in Markov Chain Monte Carlo algorithms, with critical exponents remaining consistent within uncertainties.

Contribution

The paper provides the first systematic numerical analysis of the robustness of universal critical properties under different MCMC perturbations.

Findings

Universal properties remain stable under most perturbations.

Critical exponents are consistent with standard XY model.

Large truncation errors can cause deviations, but scaling corrections obscure precise assessment.

Abstract

We numerically investigate the stability of universal properties at continuous phase transitions against perturbations of the Markov Chain Monte Carlo algorithm used to simulate the system. We consider the three dimensional XY model as test bed, and both local (single site Metropolis) and global (single cluster) updates, introducing deterministic truncation-like perturbations and stochastic perturbations in the acceptance probabilities. In (almost) all the cases we find a remarkable stability of the universal properties, even against large perturbations of the Markov Chain Monte Carlo algorithm, with critical exponents and scaling curves consistent with those of the standard XY model within statistical uncertainties. Only for the single cluster update with very large truncation error does something different happen, but large scaling corrections prevent us from precisely assessing the critical properties of the transition, and, in particular, to understand whether the critical behavior observed corresponds to a known universality class.