Influence of long-range interactions on the critical behavior of the Ising model

TL;DR

This paper investigates how long-range interactions affect the critical behavior of the two-dimensional Ising model, combining Monte Carlo simulations and renormalization group analysis to understand their dominance and influence.

Contribution

It introduces a novel approach to quantify long-range interactions as a dimensional change, supported by Monte Carlo and renormalization group methods.

Findings

Long-range interactions dominate in the intermediate regime.

Monte Carlo results confirm the dominance of long-range interactions.

Renormalization group analysis provides a new perspective on their influence.

Abstract

We study the ferromagnetic Ising model with long-range interactions in two dimensions. We first present results of a Monte Carlo study which shows that the long-range interactions dominate over the short-range ones in the intermediate regime of interaction range. Based on a renormalization group analysis, we propose a way of computing the influence of the long-range interactions as a dimensional change.