Thin Fisher Zeroes

Abstract

Biskup et al. [Phys. Rev. Lett. 84 (2000) 4794] have recently suggested that the loci of partition function zeroes can profitably be regarded as phase boundaries in the complex temperature or field planes. We obtain the Fisher zeroes for Ising and Potts models on non-planar (``thin'') regular random graphs using this approach, and note that the locus of Fisher zeroes on a Bethe lattice is identical to the corresponding random graph. Since the number of states appears as a parameter in the Potts solution the limiting locus of chromatic zeroes is also accessible.

10 pages, 4 figures

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• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
• On the relation between p-adic and ordinary strings
• Yang-Lee Zeros of the Q-state Potts Model on Recursive Lattices
• Fat Fisher Zeroes
• The Yang-Lee zeros of the 1D Blume-Capel model on connected and non-connected rings
• Time correlation functions and Fisher zeros for q-deformed Bose gas
• Yang-Lee Zeros of the Two- and Three-State Potts Model Defined on ${\varphi }^3$ Feynman Diagrams
• Fat and Thin Fisher Zeroes
• Chromatic Zeros on the Limit $G_{\infty }^{(p,\ell )}$ of the Family $G_m^{(p,\ell )}$ of Hierarchical Graphs