Critical aspects of three-dimensional anisotropic spin-glass models

TL;DR

This paper investigates a three-dimensional anisotropic spin-glass model with bond randomness only in one direction, analyzing its phase diagram and critical behavior, and comparing it to isotropic and other anisotropic models.

Contribution

It provides the phase diagram and finite-size scaling analysis of an anisotropic 3D Ising spin-glass model, revealing universality class similarities and differences in transition temperatures.

Findings

The model shares the same universality classes as the isotropic model.

Higher transition temperature from spin-glass to paramagnetic phase at the symmetric point.

Supports a forward transition behavior contrasting the reentrant behavior of isotropic models.

Abstract

We study the $\pm J$ three-dimensional Ising model with a longitudinal anisotropic bond randomness on the simple cubic lattice. The random exchange interaction is applied only in the $z$ direction, whereas in the other two directions, $xy$ - planes, we consider ferromagnetic exchange. By implementing an effective parallel tempering scheme, we outline the phase diagram of the model and compare it to the corresponding isotropic one, as well as to a previously studied anisotropic (transverse) case. We present a detailed finite-size scaling analysis of the ferromagnetic - paramagnetic and spin glass - paramagnetic transition lines, and we also discuss the ferromagnetic - spin glass transition regime. We conclude that the present model shares the same universality classes with the isotropic model, but at the symmetric point has a considerably higher transition temperature from the spin-glass state to the paramagnetic phase. Our data for the ferromagnetic - spin glass transition line are supporting a forward behavior in contrast to the reentrant behavior of the isotropic model.