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

Abstract

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.

arXiv commentJ. Phys. Soc. Jpn. 83 (2014) in press; 5 pages, 5 figures, jpsj3.cls Ver.1.1

References in corpus (8)

• Cluster Algorithm for Vertex Models
• The Kibble-Zurek Problem: Universality and the Scaling Limit
• Non-equilibrium relaxation and interface energy of the Ising model
• Dynamic scaling at classical phase transitions approached through non-equilibrium quenching
• A quantum Monte Carlo algorithm realizing an intrinsic relaxation
• Dynamic critical exponents of Swendsen-Wang and Wolff algorithms by nonequilibrium relaxation
• A Study of Dynamic Finite Size Scaling Behavior of the Scaling Functions-Calculation of Dynamic Critical Index of Wolff Algorithm
• New quantum Monte Carlo study of quantum critical phenomena with Trotter-number-dependent finite-size scaling and non-equilibrium relaxation

Cited by in corpus (5)

• Nonequilibrium behaviors of 3D Heisenberg model in the Swendsen-Wang algorithm
• Critical nonequilibrium relaxation in the Swendsen-Wang algorithm in the Berezinsky-Kosterlitz-Thouless and weak first-order phase transitions
• Critical Nonequilibrium Cluster-flip Relaxations in Ising Models
• Nonequilibrium-relaxation approach to quantum phase transitions: Nontrivial critical relaxation in cluster-update quantum Monte Carlo
• Temperature scaling in nonequilibrium relaxation in three-dimensional Heisenberg model in the Swendsen-Wang and Metropolis algorithms