# New Nonequilibrium-to-Equilibrium Dynamical Scaling and Stretched-Exponential Critical Relaxation in Cluster Algorithms

@article{Nonomura2014NewND, title={New Nonequilibrium-to-Equilibrium Dynamical Scaling and Stretched-Exponential Critical Relaxation in Cluster Algorithms}, author={Yoshihiko Nonomura}, journal={arXiv: Statistical Mechanics}, year={2014} }

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… Expand

#### 3 Citations

Critical nonequilibrium cluster-flip relaxations in Ising models

- Physics
- Physical Review E
- 2018

We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical… Expand

Nonequilibrium-relaxation approach to quantum phase transitions: Nontrivial critical relaxation in cluster-update quantum Monte Carlo.

- Mathematics, Physics
- Physical review. E
- 2020

It is shown that the NER process in classical spin systems based on cluster- update algorithms is characterized by stretched-exponential critical relaxation, rather than conventional power-law relaxation in local-update algorithms, in quantum phase transitions analyzed with the cluster-update QMC. Expand

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

- Medicine, Physics
- Physical review. E
- 2020

This study generalizes the nonequilibrium-to-equilibrium scaling scheme to off-critical relaxation process and scale relaxation data for various temperatures in the whole simulation-time regions and investigates the three-dimensional classical Heisenberg model previously analyzed with this scheme. Expand

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