Spin models with random anisotropy and reflection symmetry

Details Spin models with random anisotropy and reflection symmetry Spin models with random anisotropy and reflection symmetry

2003-11-25

arxiv.org/abs/cond-mat/0311576v1

Phys.Rev.E70:036104,2004

Physics

Condensed Matter

Statistical Mechanics

28 pages, 1 fig

Scientific paper

10.1103/PhysRevE.70.036104

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.

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