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

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.

arXiv comment11 pages, 16 pdf figures, minor changes

References in corpus (17)

• Critical Phenomena and Renormalization-Group Theory
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Critical Exponents of the N-vector model
• Quantum Metropolis Sampling
• The critical exponents of the superfluid transition in He4
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Carving out OPE space and precise $O(2)$ model critical exponents
• Finite size effects on measures of critical exponents in d=3 O(N) models
• A Quantum-Quantum Metropolis Algorithm
• Introductory lectures on lattice QCD at nonzero baryon number
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Monte Carlo study of an improved clock model in three dimensions
• High Precision Measurement of the Thermal Exponent for the Three-Dimensional XY Universality Class
• High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class
• Lattice gauge theories in the presence of a linear gauge-symmetry breaking
• Quantum computation of thermal averages in the presence of a sign problem
• Three-dimensional Abelian and non-Abelian gauge Higgs theories