Monte Carlo simulation of spin models with long-range interactions

TL;DR

This paper introduces an efficient Monte Carlo algorithm for simulating long-range interacting spin models, significantly reducing computational complexity and suppressing critical slowing down, demonstrated through applications to phase transitions.

Contribution

The paper presents a novel Monte Carlo algorithm that makes simulating long-range spin models computationally feasible and effective across different systems.

Findings

Successfully simulated Kosterlitz--Thouless transition in 1D Ising chain

Analyzed crossover from Ising-like to classical critical behavior

Reduced computational complexity for long-range interactions

Abstract

An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions between this spin and the other spins in the system. In addition, critical slowing down is strongly suppressed. In order to illustrate the range of applicability of the algorithm, two specific examples are presented. First, some aspects of the Kosterlitz--Thouless transition in the one-dimensional Ising chain with inverse-square interactions are calculated. Secondly, the crossover from Ising-like to classical critical behavior in two-dimensional systems is studied for several different interaction profiles.