Interaction anisotropy and random impurities effects on the critical behaviour of ferromagnets

TL;DR

This paper investigates how interaction anisotropy and random impurities influence the critical behavior of ferromagnets, extending idealized models to more realistic scenarios with defects and anisotropic interactions.

Contribution

It introduces models that incorporate anisotropy and dilution effects, analyzing their impact on phase transition characteristics in ferromagnetic systems.

Findings

Anisotropy modifies the order of the phase transition.

Dilution can smear out the transition.

Impurities affect critical temperature and behavior.

Abstract

The theory of phase transitions is based on the consideration of "idealized" models, such as the Ising model: a system of magnetic moments living on a cubic lattice and having only two accessible states. For simplicity the interaction is supposed to be restricted to nearest--neighbour sites only. For these models, statistical physics gives a detailed description of the behaviour of various thermodynamic quantities in the vicinity of the transition temperature. These findings are confirmed by the most precise experiments. On the other hand, there exist other cases, where one must account for additional features, such as anisotropy, defects, dilution or any effect that may affect the nature and/or the range of the interaction. These features may have impact on the order of the phase transition in the ideal model or smear it out. Here we address two classes of models where the nature of the transition is altered by the presence of anisotropy or dilution.