Dynamic and static properties of the invaded cluster algorithm
摘要
Simulations of the two-dimensional Ising and 3-state Potts models at their critical points are performed using the invaded cluster (IC) algorithm. It is argued that observables measured on a sub-lattice of size l should exhibit a crossover to Swendsen-Wang (SW) behavior for l sufficiently less than the lattice size L, and a scaling form is proposed to describe the crossover phenomenon. It is found that the energy autocorrelation time tau(l,L) for an l*l sub-lattice attains a maximum in the crossover region, and a dynamic exponent z for the IC algorithm is defined according to tau_max ~ L^z. Simulation results for the 3-state model yield z=.346(.002) which is smaller than values of the dynamic exponent found for the SW and Wolff algorithms and also less than the Li-Sokal bound. The results are less conclusive for the Ising model, but it appears that z<.21 and possibly that tau_max ~ log L so that z=0 -- similar to previous results for the SW and Wolff algorithms.
关键词
引用
@article{arxiv.cond-mat/9811138,
title = {Dynamic and static properties of the invaded cluster algorithm},
author = {K. Moriarty and J. Machta and L. Y. Chayes},
journal= {arXiv preprint arXiv:cond-mat/9811138},
year = {2009}
}
备注
21 pages with 12 figures