Medium-range interactions and crossover to classical critical behavior

TL;DR

This paper investigates how increasing the interaction range R causes a transition from Ising-like to classical critical behavior, confirming theoretical predictions through renormalization theory and Monte Carlo simulations.

Contribution

It provides a detailed analysis of the range dependence of critical amplitudes and corrections to scaling, validating theoretical models with large-scale simulations.

Findings

Critical amplitudes scale with R as predicted by theory

Monte Carlo simulations confirm the crossover behavior

Corrections to scaling depend on the interaction range R

Abstract

We study the crossover from Ising-like to classical critical behavior as a function of the range R of interactions. The power-law dependence on R of several critical amplitudes is calculated from renormalization theory. The results confirm the predictions of Mon and Binder, which were obtained from phenomenological scaling arguments. In addition, we calculate the range dependence of several corrections to scaling. We have tested the results in Monte Carlo simulations of two-dimensional systems with an extended range of interaction. An efficient Monte Carlo algorithm enabled us to carry out simulations for sufficiently large values of R, so that the theoretical predictions could actually be observed.