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arXiv · 0901.2711

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

Marco Astorino·Fabrizio Canfora
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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 {\alpha} 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.

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Marco Astorino, Fabrizio Canfora. 2009-01-18. Duality and Fisher zeros in the 2D Potts model on square lattice. https://doi.org/10.1103/physreve.81.051140

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