Numerical simulation study of the dynamical behavior of the Niedermayer algorithm

Abstract

We calculate the dynamic critical exponent for the Niedermayer algorithm applied to the two-dimensional Ising and XY models, for various values of the free parameter $E_0$. For $E_0=-1$ we regain the Metropolis algorithm and for $E_0=1$ we regain the Wolff algorithm. For $-1<E_0<1$, we show that the mean size of the clusters of (possibly) turned spins initially grows with the linear size of the lattice, $L$, but eventually saturates at a given lattice size $\tilde{L}$, which depends on $E_0$. For $L>\tilde{L}$, the Niedermayer algorithm is equivalent to the Metropolis one, i.e, they have the same dynamic exponent. For $E_0>1$, the autocorrelation time is always greater than for $E_0=1$ (Wolff) and, more important, it also grows faster than a power of $L$. Therefore, we show that the best choice of cluster algorithm is the Wolff one, when compared to the Nierdermayer generalization. We also obtain the dynamic behavior of the Wolff algorithm: although not conclusive, we propose a scaling law for the dependence of the autocorrelation time on $L$.

Accepted for publication in Journal of Statistical Mechanics: Theory and Experiment

References in corpus (2)

• Dynamic critical exponents of Swendsen-Wang and Wolff algorithms by nonequilibrium relaxation
• High-Temperature Expansion of the Free Energy in the Two-Dimensional XY Model

Cited by in corpus (2)

• The design, verification, and applications of Hotspice: a Monte Carlo simulator for artificial spin ice
• Dynamical behavior of the Niedermayer algorithm applied to Potts models