Critical points in coupled Potts models and critical phases in coupled loop models

Abstract

We show how to couple two critical Q-state Potts models to yield a new self-dual critical point. We also present strong evidence of a dense critical phase near this critical point when the Potts models are defined in their completely packed loop representations. In the continuum limit, the new critical point is described by an SU(2) coset conformal field theory, while in this limit of the the critical phase, the two loop models decouple. Using a combination of exact results and numerics, we also obtain the phase diagram in the presence of vacancies. We generalize these results to coupling two Potts models at different Q.

23 pages, 10 figures

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• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Non compact continuum limit of two coupled Potts models
• Projected Entangled Pair States with continuous virtual symmetries
• On truncations of the Chalker-Coddington model
• Critical points in coupled Potts models and correlated percolation
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder
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• One-Dimensional Sums and Finitized Characters of $2\times 2$ Fused RSOS Models
• Coulomb Gas Partition Function of a Layered Loop Model
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