Canonical local algorithms for spin systems: Heat Bath and Hasting's methods

TL;DR

This paper introduces new fast local algorithms for spin systems, using discretization and memory storage, showing advantages over existing methods for many models except the Ising +/-1 spins.

Contribution

The paper presents novel canonical local algorithms for a wide range of spin systems, improving computational efficiency through discretization and pre-stored information.

Findings

Algorithms perform favorably compared to known methods for many models.

New procedures are effective for both discrete and continuous spin systems.

Discretization scheme enables efficient simulation of complex models.

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 \phi^4 Ising model (N=1), the XY model (N=2), the Heisenberg model (N=3), the \phi^4 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 N\ge5.