Eur. Phys. J. B 41, 395-412 (2004)
https://doi.org/10.1140/epjb/e2004-00332-5

Canonical local algorithms for spin systems: heat bath and Hasting's methods

¹ Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
² Japan Science and Technology Agency, Sendai 980-8577, Japan
³ Surface Physics Laboratory, Fudan University, Shanghai 200433, P.R. China

Corresponding author: ^a Damien.Loison@physik.fu-berlin.de

Received: 25 February 2004
Revised: 16 August 2004
Published online: 21 October 2004

Abstract

We introduce new fast canonical local algorithms for discrete and continuous spin systems. We show that for a broad selection of spin systems they compare favorably to the known ones except for the Ising ±1 spins. The new procedures use discretization scheme and the necessary information have to be stored in computer memory before the simulation. The models for testing discrete spins are the Ising ±1, the general Ising S or Blume-Capel model, the Potts and the clock models. The continuous spins we examine are the O(N) models, including the continuous Ising model (N=1), the  Ising model (N=1), the XY model (N=2), the Heisenberg model (N=3), the  Heisenberg model (N=3), the O(4) model with applications to the SU(2) lattice gauge theory, and the general O(N) vector spins with .