T=0 Partition Functions for Potts Antiferromagnets on Moebius Strips and Effects of Graph Topology

Abstract

We present exact calculations of the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently the chromatic polynomial) for Moebius strips, with width $L_y=2$ or 3, of regular lattices and homeomorphic expansions thereof. These are compared with the corresponding partition functions for strip graphs with (untwisted) periodic longitudinal boundary conditions.

9 pages, Latex, Phys. Lett. A, in press

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• Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice
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• $q$-Plane Zeros of the Potts Partition Function on Diamond Hierarchical Graphs
• Zeros of Jones Polynomials for Families of Knots and Links
• Potts Model Partition Functions for Self-Dual Families of Strip Graphs
• Ground State Entropy of the Potts Antiferromagnet with Next-Nearest-Neighbor Spin-Spin Couplings on Strips of the Square Lattice
• T=0 Partition Functions for Potts Antiferromagnets on Lattice Strips with Fully Periodic Boundary Conditions
• Ground State Entropy of the Potts Antiferromagnet on Triangular Lattice Strips
• Exact Partition Function for the Potts Model with Next-Nearest Neighbor Couplings on Strips of the Square Lattice
• Reliability Polynomials and their Asymptotic Limits for Families of Graphs
• Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice
• General Structural Results for Potts Model Partition Functions on Lattice Strips
• Transfer Matrices for the Partition Function of the Potts Model on Cyclic and Mobius Lattice Strips
• Transfer Matrices for the Partition Function of the Potts Model on Toroidal Lattice Strips
• Chromatic Polynomials for Lattice Strips with Cyclic Boundary Conditions
• Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips
• Transfer Matrices for the Zero-Temperature Potts Antiferromagnet on Cyclic and Mobius Lattice Strips
• Exact Chromatic Polynomials for Toroidal Chains of Complete Graphs
• Asymptotic Behavior of Acyclic and Cyclic Orientations of Directed Lattice Graphs
• Lower Bounds on the Ground State Entropy of the Potts Antiferromagnet on Slabs of the Simple Cubic Lattice
• Improved Lower Bounds on the Ground-State Entropy of the Antiferromagnetic Potts Model
• Potts Partition Function Zeros and Ground State Entropy on Hanoi Graphs
• Exact Results for Average Cluster Numbers in Bond Percolation on Infinite-Length Lattice Strips