Spin models with random anisotropy and reflection symmetry

TL;DR

This paper investigates the critical behavior of cubic-symmetric spin systems with reflection-symmetric disorder, demonstrating that their continuous phase transitions belong to the random-exchange Ising universality class through nonperturbative and high-loop renormalization-group analyses.

Contribution

It provides a nonperturbative proof and a five-loop renormalization-group analysis showing the stability of the random-exchange Ising fixed point for these systems.

Findings

The stable fixed point is the random-exchange Ising universality class.

The critical behavior is governed by the same universality class if the transition is continuous.

Scaling corrections decay with an exponent related to the specific-heat exponent of the random-exchange Ising model.

Abstract

We study the critical behavior of a general class of cubic-symmetric spin systems in which disorder preserves the reflection symmetry $s_a\to -s_a$, $s_b\to s_b$ for $b\not= a$. This includes spin models in the presence of random cubic-symmetric anisotropy with probability distribution vanishing outside the lattice axes. Using nonperturbative arguments we show the existence of a stable fixed point corresponding to the random-exchange Ising universality class. The field-theoretical renormalization-group flow is investigated in the framework of a fixed-dimension expansion in powers of appropriate quartic couplings, computing the corresponding $\beta$-functions to five loops. This analysis shows that the random Ising fixed point is the only stable fixed point that is accessible from the relevant parameter region. Therefore, if the system undergoes a continuous transition, it belongs to the random-exchange Ising universality class. The approach to the asymptotic critical behavior is controlled by scaling corrections with exponent $\Delta = - \alpha_r$, where $\alpha_r\simeq -0.05$ is the specific-heat exponent of the random-exchange Ising model.