Duality and Regge trajectories in the 2D Potts model on square lattice

A unified approach to the ferromagnetic two dimensional Potts model on square lattice is proposed. The compatibility with the still to be found solutions of the three (and higher) dimensional Ising model allows one to write down an explicit analytic ansatz for the free energy in terms of few q-dependent Regge trajectories. The duality symmetry of the 2D Potts model together with the known results on its critical exponent α allow to fix a priori in an analytic way all but one Regge trajectory. The agreement of proposed analytic ansatz with Monte Carlo data and observations in the q = 3 case is remarkable in all the range of temperatures. It is shown that the q > 4 cases naturally fit into the same scheme and that one should also expect a good agreement with Monte Carlo data and observations. The limiting q = 4 case is shortly discussed. Keyword: Regge theory, Potts Model, Ising model, duality. PACS: 12.40.Nn,11.55.Jy, 05.20.-y, 05.70.Fh. CECS-PHY-09/0? Introduction The Potts model is the most natural generalization of the two dimensional Ising model: in the Potts model, the spin may have q different states instead of two as in the Ising case. It is one of the most interesting models in statistical mechanics and field theory and it is still waiting for an exact solutions (for a nice review see [1]). The Potts model has many interesting features and a very rich phase diagram (due to the presence of two physical parameters: the inverse temperature β and the number of states q) which can be also useful as a model marco.astorino AT gmail.com canfora AT cecs.cl In the present paper we will only consider spin models on regular square lattices.