In this work, we study the annealed Potts model coupled to two-dimensional causal triangulations (CTs). Employing duality of graphs, we prove that in the thermodynamic limit, the Potts model coupled… Click to show full abstract
In this work, we study the annealed Potts model coupled to two-dimensional causal triangulations (CTs). Employing duality of graphs, we prove that in the thermodynamic limit, the Potts model coupled to causal triangulations with parameters β and μ is equivalent to a Potts model coupled to dual causal triangulations at the dual parameters β* = log(1 + q/(eβ − 1)) and μ* = μ − 3/2log(eβ − 1) + log q. This duality relation follows from the Fermi–Kurie representation for the Potts model. Employing our duality relation, we determine a region where the critical curve for the annealed model can be located. We also provide lower and upper bounds for the infinite-volume free energy.
               
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