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

TL;DR

This paper extends the nonequilibrium-to-equilibrium scaling scheme to off-critical relaxation in the 3D Heisenberg model, enabling analysis of relaxation data across all times and temperatures in cluster and local-update algorithms.

Contribution

It introduces the first off-critical scaling method for cluster algorithms, broadening the applicability of NE-ES to nonequilibrium relaxation analysis.

Findings

Successfully scaled relaxation data across temperatures in the 3D Heisenberg model.

Demonstrated the method's effectiveness in both Swendsen-Wang and Metropolis algorithms.

Extended NE-ES to off-critical regimes, not described by traditional finite-size scaling.

Abstract

Recently, the present authors proposed the nonequilibrium-to-equilibrium scaling (NE-ES) scheme for critical Monte Carlo relaxation process, 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 is the first proposal of the off-critical scaling in cluster algorithms, which 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 Heisenberg model previously analyzed with the NE-ES [Y. Nonomura and Y. Tomita, Phys. Rev. E 93, 012101 (2016)] in the Swendsen-Wang and Metropolis algorithms.