Crossover critical behavior in the three-dimensional Ising model

TL;DR

This paper investigates the crossover from mean-field to fluctuation-driven critical behavior in the three-dimensional Ising model, using a crossover Landau model and numerical data without adjustable parameters.

Contribution

It introduces a crossover Landau model that accurately describes the critical behavior transition in the 3D Ising model across various interaction ranges without fitting parameters.

Findings

Crossover behavior analyzed over ten orders of magnitude in temperature distance.

The model matches numerical results for susceptibility and order parameter.

Dependence of the coupling constant on interaction range discussed.

Abstract

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed