We present a new cluster-update Monte Carlo algorithm for a fluctuating interface in the 3D Ising model. Critical slowing down is drastically reduced and the dynamical critical exponent at the roughening temperature of the 3D Ising model is found to be ${\mathit{z}}_{\mathrm{cl}}$ =0.44\ifmmode\pm\else\textpm\fi{}0.03. For the Metropolis algorithm we obtain ${\mathit{z}}_{\mathrm{Met}}$ =2.0\ifmmode\pm\else\textpm\fi{}0.1 while the Swendsen-Wang algorithm performs even worse than local updating. A new method which suppresses fluctuations in the two bulk phases is introduced to determine moments of the interfacial thickness.We present a new cluster-update Monte Carlo algorithm for a fluctuating interface in the 3D Ising model. Critical slowing down is drastically reduced and the dynamical critical exponent at the roughening temperature of the 3D Ising model is found to be ${\mathit{z}}_{\mathrm{cl}}$=0.44\ifmmode\pm\else\textpm\fi{}0.03. For the Metropolis algorithm we obtain ${\mathit{z}}_{\mathrm{Met}}$=2.0\ifmmode\pm\else\textpm\fi{}0.1 while the Swendsen-Wang algorithm performs even worse than local updating. A new method which suppresses fluctuations in the two bulk phases is introduced to determine moments of the interfacial thickness.

Physical Review LettersFeb 4, 199136 citations

Dynamic critical exponent of the three-dimensional XY model

Suhk Kun Oh

AIP conference proceedingsJan 1, 20010 citations

Dynamic critical exponent of three-dimensional XY model

B Kim

Physica B Condensed MatterJul 1, 20003 citations

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

Matteo Bacci, Claudio Bonati

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.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.

arXiv:2506.18561Physical review. EAug 26, 20250 citations

{\mathit{z}}_{\mathrm{cl}}

=0.44\ifmmode\pm\else\textpm\fi{}0.03. For the Metropolis algorithm we obtain

{\mathit{z}}_{\mathrm{Met}}

=2.0\ifmmode\pm\else\textpm\fi{}0.1 while the Swendsen-Wang algorithm performs even worse than local updating. A new method which suppresses fluctuations in the two bulk phases is introduced to determine moments of the interfacial thickness.