Complex-temperature phase diagrams for theq-state Potts model on self-dual families of graphs and the nature of theq→∞limit

2001/07/04 by Shu-Chiuan Chang, Robert Shrock · 5 citations
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.64.066116

published as Phys. Rev. E 64, 066116 (16 pages) (2001) · 38 pages, latex, postscript figures included

arxiv created 2001/07/04 · openalex publication_date 2001/11/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Exact calculations of the Potts model partition function Z(G,q,v) have been presented for arbitrary q and temperature-like variable v on self-dual strip graphs G of the square lattice with fixed width L(y) and arbitrarily great length Lx with two types of boundary conditions. Letting Lx-->infinity, the resultant free energy and complex-temperature phase diagram have been computed, including the locus B where the free energy is nonanalytic. Results are analyzed for widths L(y)=1,2,3. These results have been used to study the approach to the large-q limit of B.

Citations

• Modern Graph Theory
• Some generalized order-disorder transformations
• A Contribution to the Theory of Chromatic Polynomials

Cited by

• Transfer-matrix approach to three-dimensional bond percolation: An application of Novotny’s formalism
• General structural results for Potts model partition functions on lattice strips
• PARTITION FUNCTION ZEROS OF A RESTRICTED POTTS MODEL ON SELF-DUAL STRIPS OF THE SQUARE LATTICE
• Asymptotic behavior of acyclic and cyclic orientations of directed lattice graphs
• Asymptotic behavior of spanning forests and connected spanning subgraphs on two-dimensional lattices