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

Martino De Prato·Andrea Pelissetto·Ettore Vicari
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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 $ϕ_3 = 0.601(10)$ for the experimentally relevant case N=2 (XY model). The corresponding exponent $β_3 = 1.413(10)$ 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.

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Martino De Prato, Andrea Pelissetto, Ettore Vicari. 2003-02-07. Third-harmonic exponent in three-dimensional N-vector models. https://doi.org/10.1103/physrevb.68.092403

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