Non compact continuum limit of two coupled Potts models

Abstract

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.

arXiv comment33 pages, 10 figures v2: reference added, minor typo corrected v3: revised version for publication in JSTAT: section 3.1 added, some technical content moved to appendix

References in corpus (24)

• Critical Behavior of Random Bond Potts Models
• Critical Behaviour of Random Bond Potts Models: A Transfer Matrix Study
• Branes in the 2D black hole
• Renormalisation group calculation of correlation functions for the 2D random bond Ising and Potts models
• The Partition Function of the Two-Dimensional Black Hole Conformal Field Theory
• The antiferromagnetic transition for the square-lattice Potts model
• Conformal boundary loop models
• An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
• Weak Randomness for large q-State Potts models in Two Dimensions
• Coupled Potts models: Self-duality and fixed point structure
• R-matrices and Spectrum of Vertex Models based on Superalgebras
• Hecke algebraic approach to the reflection equation for spin chains
• The $Z_2$ staggered vertex model and its applications
• Character decomposition of Potts model partition functions. I. Cyclic geometry
• On $A_{n-1}^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)},A_{2n}^{(2)},A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ Reflection $K$-Matrices
• Critical RSOS Models in External Fields
• Non-Linear Integral Equations for the SL(2,R)/U(1) black hole sigma model
• New R-matrices from Representations of Braid-Monoid Algebras based on Superalgebras
• Critical points in coupled Potts models and critical phases in coupled loop models
• An integrable modification of the critical Chalker-Coddington network model
• Applications of Temperley-Lieb algebras to Lorentz lattice gases
• Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model
• Tutte chromatic identities from the Temperley-Lieb algebra
• Reflection matrices for the $U_q[sl(m|n{)}^{(1)}]$ vertex model

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