We use scale invariant scattering theory to exactly determine the renormalization group fixed points of a q-state Potts model coupled to an r-state Potts model in two dimensions. For integer values of q and r the fixed point equations are very constraining and show in particular that scale invariance in coupled Potts ferromagnets is limited to the Ashkin-Teller case (q = r = 2). Since our results extend to continuous values of the number of states, we can access the limit r -> 1 corresponding to correlated percolation, and show that the critical properties of Potts spin clusters cannot in general be obtained from those of Fortuin-Kasteleyn clusters by analytical continuation.
Critical points in coupled Potts models and correlated percolation / Lamsen, Noel; Diouane, Youness; Delfino, Gesualdo. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2023:1(2023), pp. 1-30. [10.1088/1742-5468/aca901]
Critical points in coupled Potts models and correlated percolation
Lamsen, Noel;Diouane, Youness;Delfino, Gesualdo
2023-01-01
Abstract
We use scale invariant scattering theory to exactly determine the renormalization group fixed points of a q-state Potts model coupled to an r-state Potts model in two dimensions. For integer values of q and r the fixed point equations are very constraining and show in particular that scale invariance in coupled Potts ferromagnets is limited to the Ashkin-Teller case (q = r = 2). Since our results extend to continuous values of the number of states, we can access the limit r -> 1 corresponding to correlated percolation, and show that the critical properties of Potts spin clusters cannot in general be obtained from those of Fortuin-Kasteleyn clusters by analytical continuation.File | Dimensione | Formato | |
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