Duality and Fisher zeros in the 2D Potts model on square lattice

Abstract

A phenomenological approach to the ferromagnetic two dimensional Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q-state Potts model. The duality symmetry of the 2D Potts model together with the known results on its critical exponent α allow to fix consistently the details of the proposed expression for the free energy. The agreement of the analytic ansatz with numerical data in the q=3 case is very good at high and low temperatures as well as at the critical point. It is shown that the q>4 cases naturally fit into the same scheme and that one should also expect a good agreement with numerical data. The limiting q=4 case is shortly discussed.

16 pages, 2 figures; Title changed; The main text has been clarified; Some technical points have been analyzed in more details; References added. Accepted for pubblication of PHYSICAL REVIEW E.

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Cited by in corpus (2)

• Integrable Floquet dynamics
• Potts model on recursive lattices: some new exact results