Potts model coupled to random causal triangulations

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/(e^β - 1)) and μ^∗ = μ - 3/2log(e^β - 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.