Non compact continuum limit of two coupled Potts models

Eric Vernier (1, 2) , Jesper Lykke Jacobsen (2) , Hubert Saleur (1, 3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
3 Department of Physics and Astronomy [USC, Los Angeles]

We study two $Q$-state Potts models coupled by the product of their energy operators, in the regime $2 < Q \le 4$ where the coupling is relevant. A particular choice of weights on the square lattice is shown to be equivalent to the integrable $a_3^{(2)}$ vertex model. It corresponds to a selfdual system of two antiferromagnetic Potts models, coupled ferromagnetically. We derive the Bethe Ansatz equations and study them numerically for two arbitrary twist angles. The continuum limit is shown to involve two compact bosons and one non compact boson, with discrete states emerging from the continuum at appropriate twists. The non compact boson entails strong logarithmic corrections to the finite-size behaviour of the scaling levels, the understanding of which allows us to correct an earlier proposal for some of the critical exponents. In particular, we infer the full set of magnetic scaling dimensions (watermelon operators) of the Potts model.

Domains: Statistical Mechanics [cond-mat.stat-mech]; Mathematical Physics [math-ph]; Mathematical Physics [math-ph]

Eric Vernier, Jesper Lykke Jacobsen, Hubert Saleur. Non compact continuum limit of two coupled Potts models. Journal of Statistical Mechanics: Theory and Experiment, 2014, 2014, pp.P10003. ⟨cea-01065025⟩