Critical behavior of the random-anisotropy model in the strong-anisotropy limit

TL;DR

This paper studies the critical behavior of the strong-anisotropy limit of the random-anisotropy Heisenberg model, using Monte Carlo simulations to identify a finite-temperature phase transition and universality class similarities with Ising spin glasses.

Contribution

It provides the first detailed Monte Carlo analysis of the SRAM, revealing critical exponents and confirming its universality class with uncorrelated bond disorder Ising spin glasses.

Findings

Evidence of a finite-temperature continuous transition.

Critical exponents close to those of the Ising spin-glass model.

Leading correction-to-scaling exponent determined as ω=1.0(4).

Abstract

We investigate the nature of the critical behavior of the random-anisotropy Heisenberg model (RAM), which describes a magnetic system with random uniaxial single-site anisotropy, such as some amorphous alloys of rare earths and transition metals. In particular, we consider the strong-anisotropy limit (SRAM), in which the Hamiltonian can be rewritten as the one of an Ising spin-glass model with correlated bond disorder. We perform Monte Carlo simulations of the SRAM on simple cubic L^3 lattices, up to L=30, measuring correlation functions of the replica-replica overlap, which is the order parameter at a glass transition. The corresponding results show critical behavior and finite-size scaling. They provide evidence of a finite-temperature continuous transition with critical exponents $\eta_o=-0.24(4)$ and $\nu_o=2.4(6)$. These results are close to the corresponding estimates that have been obtained in the usual Ising spin-glass model with uncorrelated bond disorder, suggesting that the two models belong to the same universality class. We also determine the leading correction-to-scaling exponent finding $\omega = 1.0(4)$.