Ground State Entropy and the $q=3$ Potts Antiferromagnet on the Honeycomb Lattice

Abstract

We study the $q$-state Potts antiferromagnet with $q=3$ on the honeycomb lattice. Using an analytic argument together with a Monte Carlo simulation, we conclude that this model is disordered for all $T\ge 0$. We also calculate the ground state entropy to be $S_0/k_B=0.507(10)$ and discuss this result.

9 pages, latex, with two eps figures

References in corpus (1)

• Antiferromagnetic Potts Models on the Square Lattice

Cited by in corpus (33)

• Asymptotic Limits and Zeros of Chromatic Polynomials and Ground State Entropy of Potts Antiferromagnets
• Exact Potts Model Partition Functions on Ladder Graphs
• Three-dimensional antiferromagnetic q-state Potts models: application of the Wang-Landau algorithm
• Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals
• The 3-State Square-Lattice Potts Antiferromagnet at Zero Temperature
• Chromatic Polynomials for $J(\prod H)I$ Strip Graphs and their Asymptotic Limits
• Ground State Entropy of Potts Antiferromagnets: Homeomorphic Classes with Noncompact W Boundaries
• Ground State Entropy of Potts Antiferromagnets on Homeomorphic Families of Strip Graphs
• Families of Graphs with W_r({G},q) Functions That Are Nonanalytic at 1/q=0
• Study of the Potts Model on the Honeycomb and Triangular Lattices: Low-Temperature Series and Partition Function Zeros
• Ground State Entropy of Potts Antiferromagnets: Cases with Noncompact W Boundaries Having Multiple Points at 1/q = 0
• Ground-State Degeneracy of Potts Antiferromagnets on Two-Dimensional Lattices: Approach Using Infinite Cyclic Strip Graphs
• Ground State Entropy of Potts Antiferromagnets and the Approach to the 2D Thermodynamic Limit
• Upper and Lower Bounds for Ground State Entropy of Antiferromagnetic Potts Models
• Families of Graphs With Chromatic Zeros Lying on Circles
• Ground State Entropy of Potts Antiferromagnets: Bounds, Series, and Monte Carlo Measurements
• Exact Potts Model Partition Functions on Strips of the Honeycomb Lattice
• Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs
• 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
• Random Matrices and the Convergence of Partition Function Zeros in Finite Density QCD
• A Mapping Relating Complex and Physical Temperatures in the 2D $q$-state Potts Model and Some Applications
• The Hintermann-Merlini-Baxter-Wu and the Infinite-Coupling-Limit Ashkin-Teller Models
• Monte Carlo study of the antiferromagnetic three-state Potts model with staggered polarization field on the square lattice
• The 3-State Potts Antiferromagnet on the Hexagonal Lattice
• A condition for long-range order in discrete spin systems with application to the antiferromagnetic Potts model
• Complex-Temperature Phase Diagrams of 1D Spin Models with Next-Nearest-Neighbor Couplings
• 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 Potts Model Partition Functions for Strips of the Honeycomb Lattice
• End Graph Effects on Chromatic Polynomials for Strip Graphs of Lattices and their Asymptotic Limits
• Potts Partition Function Zeros and Ground State Entropy on Hanoi Graphs
• Ground State Entropy in Potts Antiferromagnets and Chromatic Polynomials