Universal finite-size scaling analysis of Ising models with long-range interactions at the upper critical dimensionality: Isotropic case

TL;DR

This paper performs a finite-size scaling analysis of a 2D isotropic long-range Ising model at its upper critical dimension, demonstrating the universality of scaling functions through Monte Carlo simulations and theoretical comparisons.

Contribution

It extends the concept of universal finite-size scaling functions to the upper critical dimensionality for isotropic long-range Ising models, supported by numerical and theoretical analysis.

Findings

Excellent agreement between Monte Carlo data and mean-field scaling functions

Universal finite-size scaling functions can be applied at the upper critical dimension

Validation of the Privman-Fisher hypothesis in this context

Abstract

We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic whereby in the present work we focus on the isotropic case for which the model is found to be at its upper critical dimensionality. To investigate the critical behavior the temperature and field dependence of several quantities are studied by means of Monte Carlo simulations. On the basis of the Privman-Fisher hypothesis and results of the renormalization group the numerical data are analyzed in the framework of a finite-size scaling analysis and compared to finite-size scaling functions derived from a Ginzburg-Landau-Wilson model in zero mode (mean-field) approximation. The obtained excellent agreement suggests that at least in the present case the concept of universal finite-size scaling functions can be extended to the upper critical dimensionality.