Condensation and Metastability in the 2D Potts Model

Details Condensation and Metastability in the 2D Potts Model Condensation and Metastability in the 2D Potts Model

1999-03-29

arxiv.org/abs/cond-mat/9903413v1

Eur.Phys.J.B13:341-352,2000

Physics

Condensed Matter

Statistical Mechanics

32 pages, 6 figures, Latex

Scientific paper

10.1007/s100510050040

For the first order transition of the Ising model below $T_c$, Isakov has proven that the free energy possesses an essential singularity in the applied field. Such a singularity in the control parameter, anticipated by condensation theory, is believed to be a generic feature of first order transitions, but too weak to be observable. We study these issues for the temperature driven transition of the $q$ states 2D Potts model at $q>q_c=4$. Adapting the droplet model to this case, we relate its parameters to the critical properties at $q_c$ and confront the free energy to the many informations brought by previous works. The essential singularity predicted at the transition temperature leads to observable effects in numerical data. On a finite lattice, a metastability domain of temperatures is identified, which shrinks to zero in the thermodynamical limit. ~

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