Spin models with random anisotropy and reflection symmetry

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 $b\ne a$. 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.

28 pages, 1 fig

References in corpus (6)

• Multicritical phenomena in O(n_1)+O(n_2)-symmetric theories
• The three-dimensional randomly dilute Ising model: Monte Carlo results
• Frozen Quasi Long Range Order in Random Anisotropy Heisenberg Magnet
• Crossover behavior in three-dimensional dilute spin systems
• Crossover from random-exchange to random-field critical behavior in Ising models
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Cited by in corpus (10)

• Critical properties of random anisotropy magnets
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• Critical behavior of the random-anisotropy model in the strong-anisotropy limit
• Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Possibility of a continuous phase transition in random-anisotropy magnets with ageneric random-axis distribution
• Model C critical dynamics of random anisotropy magnets
• Two-loop Feynman integrals for ${\varphi }^4$ theory with long-range correlated disorder
• Critical Behavior of the Three-Dimensional Random Anisotropy Heisenberg Model
• Equilibrium and out-of-equilibrium critical dynamics of the three-dimensional Heisenberg model with random cubic anisotropy