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

Abstract

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/ν.

20 pages, 4 figures, to appear in Physica A

References in corpus (2)

• Criticality in one dimension with inverse square-law potentials
• Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q

Cited by in corpus (4)

• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
• Exact solution of a classical short-range spin model with a phase transition in one dimension: the Potts model with invisible states
• Classical phase transitions in a one-dimensional short-range spin model induced by entropy depletion or complex fields
• Yang-Lee zeros and the critical behavior of the infinite-range two- and three-state Potts models