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

  title={New Nonequilibrium-to-Equilibrium Dynamical Scaling and Stretched-Exponential Critical Relaxation in Cluster Algorithms},
  author={Yoshihiko Nonomura},
  journal={arXiv: Statistical Mechanics},
  • Y. Nonomura
  • Published 1 July 2014
  • Physics
  • arXiv: Statistical Mechanics
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

Figures from this paper

Critical nonequilibrium cluster-flip relaxations in Ising models
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 criticalExpand
Nonequilibrium-relaxation approach to quantum phase transitions: Nontrivial critical relaxation in cluster-update quantum Monte Carlo.
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.
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


Dynamic critical exponents for Swendsen–Wang and Wolff algorithms obtained by a nonequilibrium relaxation method
Using a nonequilibrium relaxation method, we calculate the dynamic critical exponent z of the two-dimensional Ising model for the Swendsen–Wang and Wolff algorithms. We examine dynamic relaxationExpand
Stretched and non-stretched exponential relaxation in Ising ferromagnets
The decay of the Hamming distance in Monte Carlo simulations of Ising models with model A dynamics is shown to be numerically efficient to investigate the dynamics also below Tc. We observe a simpleExpand
Non-equilibrium relaxation and interface energy of the Ising model
  • N. Ito
  • Mathematics, Physics
  • 1993
From the non-equilibrium critical relaxation study of the two-dimensional Ising model, the dynamical critical exponent z is estimated to be 2.165 ± 0.010 for this model. The relaxation in the orderedExpand
Single-cluster Monte Carlo dynamics for the Ising model
We present an extensive study of a new Monte Carlo acceleration algorithm introduced by Wolff for the Ising model. It differs from the Swendsen-Wang algorithm by growing and flipping single clustersExpand
Non-equilibrium critical relaxation of the three-dimensional Ising model
Abstract The non-equilibrium relaxation process at the critical point is studied using Monte Carlo simulation for the ferromagnetic Ising model on a cubic lattice. It was observed that theExpand
Nonequilibrium relaxation method
The nonequilibrium relaxation (NER) method is a numerical technique to analyse equilibrium phase transitions. One can estimate the transition point and critical exponents calculating relaxations ofExpand
A study of dynamic finite size scaling behavior of the scaling functions - calculation of dynamic critical index of Wolff algorithm
The vanishing dynamic critical exponent obtained for d = 3 implies that the Wolff algorithm is more efficient in eliminating critical slowing down in Monte Carlo simulations than previously reported. Expand
Comparison of cluster algorithms for two-dimensional Potts models.
We have measured the dynamical critical exponent {ital z} for the Swendsen-Wang and the Wolff cluster update algorithms, as well as a number of variants of these algorithms, for the {ital q}=2 andExpand
Static and Dynamic Finite-Size Scaling Theory Based on the Renormalization Group Approach
Fisher's static finite-size scaling law is derived on the basis of the renormalization group theory and it is extended to dynamic critical phenomena in a finite system. This dynamic finite-sizeExpand
Kibble-Zurek problem: Universality and the scaling limit
Near a critical point, the equilibrium relaxation time of a system diverges and any change of control/thermodynamic parameters leads to non-equilibrium behavior. The Kibble-Zurek problem is toExpand