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

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arxiv cond-mat/0302145 v1 pith:LXUK5GXO submitted 2003-02-07 cond-mat.stat-mech hep-lat

Martino De Prato , Andrea Pelissetto , Ettore Vicari This is my paper · ORCID
classification cond-mat.stat-mechhep-lat
keywords exponentmodelsthree-dimensionaltransitionagreementapproachassociatedbeta
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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 $\phi_3 = 0.601(10)$ 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.

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    A semiclassical expansion around a superfluid configuration computes Δ_{φ^n} at fixed λ*n, reproducing diagrammatic results at small λ*n and the large-charge CFT expansion at large λ*n.

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