Pseudodimensional variation and tricriticality of Potts models by hierarchical breaking of translational invariance

Potts models with equivalent- and nearest-neighbor interactions are solved exactly on Cayley trees. A parameter D is identified that plays a role similar to the spatial dimension on Bravais lattices. Breaking translational symmetry by the Cayley-tree hierarchy reduces D, leading to a changeover in the order of the phase transition via a novel tricritical point.