Critical Behavior of Vector Models with Cubic Symmetry
نویسندگان
چکیده
We report on some results concerning the effects of cubic anisotropy and quenched un-correlated impurities on multicomponent spin models. The analysis of the six-loop three-dimensional series provides an accurate description of the renormalization-group flow. 1 Cubic-symmetric models The magnetic interactions in crystalline solids with cubic symmetry like iron or nickel are usually modeled using the O(3)-symmetric Heisenberg Hamiltonian. However, this is a simplified model, since other interactions are present. Among them, the magnetic anisotropy that is induced by the lattice structure is particularly relevant experimentally. In cubic-symmetric lattices it gives rise to additional single-ion contributions, the simplest one being i s 4 i. These terms are usually not considered when the critical behavior of cubic magnets is discussed. However, this is strictly justified only if these nonrotationally invariant interactions, that have the reduced symmetry of the lattice, are irrelevant in the renormalization-group (RG) sense. This question has been extensively investigated during the past decades [1, 2]. In the field-theoretical context, one considers the φ 4 Hamiltonian and adds all cubic-invariant interactions that may be potentially relevant. There are two possible terms: a cubic hopping term µ (∂ µ φ µ) 2 and a cubic-symmetric quartic interaction term µ φ 4 µ. The first term was shown to be irrelevant, although it induces slowly-decaying crossover effects [1]. In order to study the second one, one considers a φ 4 theory with two quartic couplings [1]: H c = d d x 1 2 (∂ µ φ(x)) 2 + 1 2 rφ(x) 2 + 1 4! v 0 φ(x) 2 2 + 1 4! w 0 M i=1 φ i (x) 4 , (1) where φ is an M-vector field (M = 3 for magnets). The fixed-point (FP) structure of the model (1) has been investigated extensively and there is a general consensus that a critical value 1
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تاریخ انتشار 2002