Third-harmonic exponent in three-dimensional N-vector models

Abstract

We compute the crossover exponent associated with the spin-3 operator in three-dimensional O(N) models. A six-loop field-theoretical calculation in the fixed-dimension approach gives ${\varphi }_3=0.601(10)$ for the experimentally relevant case N=2 (XY model). The corresponding exponent ${\beta }_3=1.413(10)$ is compared with the experimental estimates obtained in materials undergoing a normal-incommensurate structural transition and in liquid crystals at the smectic-A--hexatic-B phase transition, finding good agreement.

6 pages

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• Conformal dimensions via large charge expansion
• Three-dimensional antiferromagnetic CP(N-1) models
• Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach
• Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories