Dynamic critical exponents of Swendsen-Wang and Wolff algorithms by nonequilibrium relaxation
arXiv:cond-mat/0603038 · doi:10.1088/1742-5468/2006/05/P05004
Abstract
With 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 relaxation processes following a quench from a disordered or an ordered initial state to the critical temperature T_c, and measure the exponential relaxation time of the system energy. For the Swendsen-Wang algorithm with an ordered or a disordered initial state, and for the Wolff algorithm with an ordered initial state, the exponential relaxation time fits well to a logarithmic size dependence up to a lattice size L=8192. For the Wolff algorithm with a disordered initial state, we obtain an effective dynamic exponent z_exp=1.19(2) up to L=2048. For comparison, we also compute the effective dynamic exponents through the integrated correlation times. In addition, an exact result of the Swendsen-Wang dynamic spectrum of a one-dimension Ising chain is derived.
13 pages, 6 figures
References in corpus (4)
- Dynamic critical behavior of the Swendsen--Wang Algorithm for the three-dimensional Ising model
- Comments on Sweeny and Gliozzi dynamics for simulations of Potts models in the Fortuin-Kasteleyn representation
- A Study of Dynamic Finite Size Scaling Behavior of the Scaling Functions-Calculation of Dynamic Critical Index of Wolff Algorithm
- Dynamical Critical Behaviors of the Ising Spin Chain: Swendsen-Wang and Wolff Algorithms
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