  In this work we study the annealed Potts model coupled to two dimensional
causal triangulations with periodic boundary condition. Using duality on a
torus, we provide a relation between the free energy of the Potts model coupled
CTs and its dual. This duality relation follows from the FK representation for
the Potts model. In order to determine a region where the critical curve for
the model can be located we use the duality relation and the high-temperature
expansion. This is done by outlining a region where the infinite-volume Gibbs
measure exists and is unique and a region where the finite-volume Gibbs mea-
sure has no weak limit (in fact, does not exist if the volume is large enough).
We also provide lower and upper bounds for the infinite- volume free energy.
