Zeros of the Potts Model Partition Function on Sierpinski Graphs

Abstract

We calculate zeros of the $q$-state Potts model partition function on $m$'th-iterate Sierpinski graphs, $S_m$, in the variable $q$ and in a temperature-like variable, $y$. We infer some asymptotic properties of the loci of zeros in the limit $m\to \infty$ and relate these to thermodynamic properties of the $q$-state Potts ferromagnet and antiferromagnet on the Sierpinski gasket fractal, $S_{\infty }$.

6 pages, 8 figures

References in corpus (11)

• Spanning trees on the Sierpinski gasket
• Asymptotic Limits and Zeros of Chromatic Polynomials and Ground State Entropy of Potts Antiferromagnets
• Exact Potts Model Partition Functions on Ladder Graphs
• Exact Potts Model Partition Function on Strips of the Triangular Lattice
• The Julia sets and complex singularities in hierarchical Ising models
• Ground-State Degeneracy of Potts Antiferromagnets on Two-Dimensional Lattices: Approach Using Infinite Cyclic Strip Graphs
• Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices
• Complex-Temperature Phase Diagrams for the q-State Potts Model on Self-Dual Families of Graphs and the Nature of the $q\to \infty$ Limit
• Potts Model Partition Functions for Self-Dual Families of Strip Graphs
• Distribution and density of the partition function zeros for the diamond-decorated Ising model
• Zeros of the Potts Model Partition Function in the Large-$q$ Limit

Cited by in corpus (10)

• Overfrustrated and Underfrustrated Spin-Glasses in d=3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d=2
• Odd q-State Clock Spin-Glass Models in Three Dimensions, Asymmetric Phase Diagrams, and Multiple Algebraically Ordered Phases
• $q$-Plane Zeros of the Potts Partition Function on Diamond Hierarchical Graphs
• Lower-Critical Spin-Glass Dimension from 23 Sequenced Hierarchical Models
• The Chiral Potts Spin Glass in d=2 and 3 Dimensions
• Exact solution of a classical short-range spin model with a phase transition in one dimension: the Potts model with invisible states
• Stepwise Positional-Orientational Order and the Multicritical-Multistructural Global Phase Diagram of the s=3/2 Ising Model from Renormalization-Group Theory
• Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket
• Potts Partition Function Zeros and Ground State Entropy on Hanoi Graphs
• Chromatic Zeros on the Limit $G_{\infty }^{(p,\ell )}$ of the Family $G_m^{(p,\ell )}$ of Hierarchical Graphs