Upper and Lower Bounds for Ground State Entropy of Antiferromagnetic Potts Models

Abstract

We derive rigorous upper and lower bounds for the ground state entropy of the $q$-state Potts antiferromagnet on the honeycomb and triangular lattices. These bounds are quite restrictive, especially for large $q$.

8 pages, latex, with two eps figures

Cited by in corpus (29)

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• Ground State Entropy of Potts Antiferromagnets: Homeomorphic Classes with Noncompact W Boundaries
• Structural Properties of Potts Model Partition Functions and Chromatic Polynomials for Lattice Strips
• Study of the Potts Model on the Honeycomb and Triangular Lattices: Low-Temperature Series and Partition Function Zeros
• Families of Graphs with W_r({G},q) Functions That Are Nonanalytic at 1/q=0
• Ground State Entropy of Potts Antiferromagnets: Cases with Noncompact W Boundaries Having Multiple Points at 1/q = 0
• T=0 Partition Functions for Potts Antiferromagnets on Moebius Strips and Effects of Graph Topology
• Ground State Entropy of Potts Antiferromagnets and the Approach to the 2D Thermodynamic Limit
• Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice
• Ground State Entropy of Potts Antiferromagnets: Bounds, Series, and Monte Carlo Measurements
• Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs
• Complex-Temperature Partition Function Zeros of the Potts Model on the Honeycomb and Kagomé Lattices
• Ground State Entropy of the Potts Antiferromagnet with Next-Nearest-Neighbor Spin-Spin Couplings on Strips of the Square Lattice
• Potts Model Partition Functions for Self-Dual Families of Strip Graphs
• Ground State Entropy of the Potts Antiferromagnet on Triangular Lattice Strips
• A Mapping Relating Complex and Physical Temperatures in the 2D $q$-state Potts Model and Some Applications
• Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice
• The 3-State Potts Antiferromagnet on the Hexagonal Lattice
• Transfer Matrices for the Zero-Temperature Potts Antiferromagnet on Cyclic and Mobius Lattice Strips
• Large-q series expansion for the ground state degeneracy of the q-state Potts antiferromagnet on the (3.12^2) lattice
• Exact Chromatic Polynomials for Toroidal Chains of Complete Graphs
• Asymptotic Behavior of Acyclic and Cyclic Orientations of Directed Lattice Graphs
• Study of Exponential Growth Constants of Directed Heteropolygonal Archimedean Lattices
• Lower Bounds on the Ground State Entropy of the Potts Antiferromagnet on Slabs of the Simple Cubic Lattice
• Potts Partition Function Zeros and Ground State Entropy on Hanoi Graphs
• Improved Lower Bounds on the Ground-State Entropy of the Antiferromagnetic Potts Model
• Ground State Entropy in Potts Antiferromagnets and Chromatic Polynomials