Dynamic critical exponents of Swendsen-Wang and Wolff algorithms by nonequilibrium relaxation
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.
Keywords
Cite
@article{arxiv.cond-mat/0603038,
title = {Dynamic critical exponents of Swendsen-Wang and Wolff algorithms by nonequilibrium relaxation},
author = {Jianqing Du and Bo Zheng and Jian-Sheng Wang},
journal= {arXiv preprint arXiv:cond-mat/0603038},
year = {2011}
}
Comments
13 pages, 6 figures