engleski

Complex-q zeros of the partition function of the Potts model with long-range interactions

We examine the loci of the partition function zeros in the complex-q plane of the ferromagnetic q-state Potts model. The detail study was performed on the mean-field limit of the model, while only a two preliminary results are given for the one-dimensional model with a long-range interactions decaying with a distance r as 1/r^{; ; ; ; 1+\sigma}; ; ; ; . In both cases, at any fixed temperature and for finite number of particles N, zeros lie on a smooth curve leaving the gap around the positive real-q axis. The gap vanishes in the N \to \infty limit. For finite and large N \gg 1 the analytic expressions for the zeros closest to the positive real-q axis and for density of zeros, have been calculated for the mean-field model. It shows that the approach to the thermodynamic limit of both closest zeros and density of zeros, depends on the order of transition. For two examples of 1/r^{; ; ; ; 1+\sigma}; ; ; ; interactions, the convergence N \to \infty of the zeros closest to the positive real-q axis has been numerically analyzed for models with N \le 9 particles.

Phase transitions ; q-state Potts model ; Complex-q zeros

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