A Study of Dynamic Finite Size Scaling Behavior of the Scaling Functions-Calculation of Dynamic Critical Index of Wolff Algorithm

Abstract

In this work we have studied the dynamic scaling behavior of two scaling functions and we have shown that scaling functions obey the dynamic finite size scaling rules. Dynamic finite size scaling of scaling functions opens possibilities for a wide range of applications. As an application we have calculated the dynamic critical exponent ($z$) of Wolff's cluster algorithm for 2-, 3- and 4-dimensional Ising models. Configurations with vanishing initial magnetization are chosen in order to avoid complications due to initial magnetization. The observed dynamic finite size scaling behavior during early stages of the Monte Carlo simulation yields $z$ for Wolff's cluster algorithm for 2-, 3- and 4-dimensional Ising models with vanishing values which are consistent with the values obtained from the autocorrelations. Especially, the vanishing dynamic critical exponent we obtained for $d=3$ implies that the Wolff algorithm is more efficient in eliminating critical slowing down in Monte Carlo simulations than previously reported.

arXiv commentLatex, 24 pages, 13 eps figures. Accepted for publication in Computer Physics Communication

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Cited by in corpus (5)

• An introduction to Monte Carlo methods
• Dynamic critical exponents of Swendsen-Wang and Wolff algorithms by nonequilibrium relaxation
• 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
• New Nonequilibrium-to-Equilibrium Dynamical Scaling and Stretched-Exponential Critical Relaxation in Cluster Algorithms