A cluster heat bath method on a quasi-onedimensional Ising model

TL;DR

The paper introduces a cluster heat bath method for a quasi-one-dimensional Ising model that accurately reproduces two-dimensional Ising model results while significantly reducing simulation time by treating chains as equilibrium entities.

Contribution

A novel cluster heat bath method for quasi-one-dimensional Ising models that simplifies simulations by leveraging equilibrium states of chains.

Findings

Reproduces exact 2D Ising model results

Reduces simulation time drastically

Effective dimensionality reduction

Abstract

We have proposed a cluster heat bath(CHB) method of a quasi-one dimensional Ising model and demonstrated that it reproduces the exact results of the two dimensional Ising model with axially anisotropic exchange interactions. The point of the method is to select one of the equilibrium spin configurations of each of the chains which are subjected by effective fields of surrounding spins. Thus the chains are always in their equilibrium state during the simulation and the $d$ dimensional model effectively becomes as a $d-1$ dimensional model of fictitious spins with their freedom of $2^N$ and the simulation time is drastically reduced, where $N$ is the number of the spins on the chain.