Simulation of Spin Glass with a Variable-system-size Ensemble

TL;DR

This paper presents a novel Monte Carlo algorithm for spin glasses that allows the system size to fluctuate, improving sampling efficiency by combining multiple canonical ensembles with a variable-system-size ensemble.

Contribution

The authors introduce a new dynamical Monte Carlo method using a variable-system-size ensemble, enhancing simulation efficiency for spin glass models compared to traditional algorithms.

Findings

The algorithm successfully simulates the SK spin glass model.

It demonstrates improved performance over conventional heat bath algorithms.

The method maintains detailed balance while allowing system size fluctuations.

Abstract

In this paper, we introduce a dynamical Monte Carlo algorithm for spin models in which the number of the spins fluctuates from zero to a given number by addition and deletion of spins with a probabilistic rule. Such simulations are realized with a variable-system-size ensemble, a mixture of canonical ensembles each of which corresponds to a system with different size. The weight of each component of the mixture is controlled by a penalty term and systematically tuned in a preliminary run in a way similar to the multicanonical algorithm. In a measurement run, the system grows and shrinks without violating the detailed balance condition and we can obtain the correct canonical averages if physical quantities is measured only when its size is equal to the prescribed maximum size. The mixing of Markov chain is facilitated by the fast relaxation at small system sizes. The algorithm is implemented for the SK model of spin glass and shows better performance than that of a conventional heat bath algorithm.