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

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

2001-11-09

arxiv.org/abs/cond-mat/0111157v2

Physica A 310 (2002) 91

Physics

Condensed Matter

Statistical Mechanics

20 pages, 4 figures, to appear in Physica A

Scientific paper

10.1016/S0378-4371(02)00742-2

The zeros of the partition function of the ferromagnetic q-state Potts model with long-range interactions in the complex-q plane are studied in the mean-field case, while preliminary numerical results are reported for the finite 1d chains with power-law decaying interactions. In both cases, at any fixed temperature, the zeros lie on the arc-shaped contours, which cross the positive real axis at the value for which the given temperature is transition temperature. For finite number of particles the positive real axis is free of zeros, which approach to it in the thermodynamic limit. The convergence exponent of the zero closest to the positive real-q axis is found to have the same value as the temperature critical exponent 1/\nu.

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