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Bulletin of the American Physical Society

Nontrivial nonequilibrium critical relaxation in cluster algorithms and universal nonequilibrium-to-equilibrium scaling procedure

Yoshihiko Nonomura, Yusuke Tomita

Published Mar 2, 2015• 0 citations
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We propose an extension of the nonequilibrium invaded cluster (IC) algorithm, which reestablishes a correct scaling of fluctuations at criticality and also self-adjusts to the critical temperature. We show that by introducing a single constraint to the intrinsic quantity of the IC algorithm the temperature becomes well defined and the sampling of the equilibrium ensemble is regained. The procedure is applied to the Potts model in two and three dimensions.

arXiv:0805.0711•Physical Review E•May 6, 2008•3 citations
Nonequilibrium relaxation behaviors in the Ising model on a square lattice based on the Wolff algorithm are totally different from those based on local-update algorithms. In particular, the critical relaxation is described by the stretched-exponential decay. We propose a novel scaling procedure to connect nonequilibrium and equilibrium behaviors continuously, and find that the stretched-exponential scaling region in the Wolff algorithm is as wide as the power-law scaling region in local-update algorithms. We also find that relaxation to the spontaneous magnetization in the ordered phase is characterized by the exponential decay, not the stretched-exponential decay based on local-update algorithms.
Recently the present authors proposed the nonequilibrium-to-equilibrium scaling (NE-ES) scheme for the critical Monte Carlo relaxation process [Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014)10.7566/JPSJ.83.113001], which scales relaxation data in the whole simulation-time regions regardless of functional forms, namely, both for the stretched-exponential critical relaxation in cluster algorithms and for the power-law critical relaxation in local-update algorithms. In the present study, we generalize this scheme to off-critical relaxation process and scale relaxation data for various temperatures in the whole simulation-time regions. This proposal of the off-critical scaling in cluster algorithms cannot be described by the dynamical finite-size scaling theory based on the power-law critical relaxation. As an example, we investigate the three-dimensional classical Heisenberg model previously analyzed with the NE-ES [Nonomura and Tomita, Phys. Rev. E 93, 012101 (2016)10.1103/PhysRevE.93.012101] in the Swendsen-Wang and Metropolis algorithms.