Coupled Potts models: Self-duality and fixed point structure

Abstract

We consider q-state Potts models coupled by their energy operators. Restricting our study to self-dual couplings, numerical simulations demonstrate the existence of non-trivial fixed points for 2 <= q <= 4. These fixed points were first predicted by perturbative renormalisation group calculations. Accurate values for the central charge and the multiscaling exponents of the spin and energy operators are calculated using a series of novel transfer matrix algorithms employing clusters and loops. These results compare well with those of the perturbative expansion, in the range of parameter values where the latter is valid. The criticality of the fixed-point models is independently verified by examining higher eigenvalues in the even sector, and by demonstrating the existence of scaling laws from Monte Carlo simulations. This might be a first step towards the identification of the conformal field theories describing the critical behaviour of this class of models.

70 pages; 17 tables and 15 figures in text. Improved numerics; Formula (3.16) and Table 2 corrected

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• Coupled minimal models revisited
• Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap
• Emerging criticality in the disordered three-color Ashkin-Teller model
• Critical interfaces in the random-bond Potts model
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• Density of states determined from Monte Carlo simulations
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Models WD_{n} in the presence of disorder and the coupled models
• Non compact continuum limit of two coupled Potts models
• Universality of coupled Potts models
• Projected Entangled Pair States with continuous virtual symmetries
• Rotations, Negative Eigenvalues, and Newton Method in Tensor Network Renormalization Group
• Critical points in coupled Potts models and correlated percolation
• Finite average lengths in critical loop models
• Nature of phase transitions in Axelrod-like coupled Potts models in two dimensions
• Coulomb Gas Partition Function of a Layered Loop Model
• Selfduality for coupled Potts models on the triangular lattice