Mean-field expansion for spin models with medium-range interactions

TL;DR

This paper develops a systematic mean-field expansion to analyze the critical crossover in O(N) spin models with medium-range interactions, providing universal curves and corrections, and compares results with Monte Carlo simulations.

Contribution

It introduces a novel systematic expansion around mean-field solutions for medium-range interactions, elucidating universal crossover behavior and leading corrections in three dimensions.

Findings

Leading correction scales as R^{-3} in three dimensions

Universal crossover curves are derived and characterized

Results are validated against Monte Carlo simulations

Abstract

We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N)-invariant spin models with medium-range interactions. We perform a systematic expansion around the mean-field solution, obtaining the universal crossover curves and their leading corrections. In particular we show that, in three dimensions, the leading correction scales as $R^{-3}, R$ being the range of the interactions. We compare our results with the existing numerical ones obtained by Monte Carlo simulations and present a critical discussion of other approaches.