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 a 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.

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• Classical statistical mechanics
• Critical phenomena
• Classical spin models
• Metropolis algorithm
• Monte Carlo methods
• Renormalization group