Temperature scaling in nonequilibrium relaxation in three-dimensional Heisenberg model in the Swendsen-Wang and Metropolis 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.