T = 0 partition functions for Potts antiferromagnets on lattice strips with fully periodic boundary conditions

Shu-Chiuan Chang, Robert Shrock

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

We present exact calculations of the zero-temperature partition function for the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) for families of arbitrarily long strip graphs of the square and triangular lattices with width Ly = 4 and boundary conditions that are doubly periodic or doubly periodic with reversed orientation (i.e., of torus or Klein bottle type). These boundary conditions have the advantage of removing edge effects. In the limit of infinite length, we calculate the exponent of the entropy, W(q) and determine the continuous locus B where it is singular. We also give results for toroidal strips involving `crossing subgraphs'; these make possible a unified treatment of torus and Klein bottle boundary conditions and enable us to prove that for a given strip, the locus B is the same for these boundary conditions.

Original languageEnglish
Pages (from-to)307-345
Number of pages39
JournalPhysica A: Statistical Mechanics and its Applications
Volume292
Issue number1-4
DOIs
Publication statusPublished - 2001 Mar 15

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Antiferromagnet
Periodic Boundary Conditions
Partition Function
Strip
partitions
strip
boundary conditions
Boundary conditions
Klein bottle
bottles
loci
Locus
Torus
Edge Effects
Chromatic Polynomial
Triangular Lattice
Square Lattice
Subgraph
polynomials
Exponent

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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abstract = "We present exact calculations of the zero-temperature partition function for the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) for families of arbitrarily long strip graphs of the square and triangular lattices with width Ly = 4 and boundary conditions that are doubly periodic or doubly periodic with reversed orientation (i.e., of torus or Klein bottle type). These boundary conditions have the advantage of removing edge effects. In the limit of infinite length, we calculate the exponent of the entropy, W(q) and determine the continuous locus B where it is singular. We also give results for toroidal strips involving `crossing subgraphs'; these make possible a unified treatment of torus and Klein bottle boundary conditions and enable us to prove that for a given strip, the locus B is the same for these boundary conditions.",
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T = 0 partition functions for Potts antiferromagnets on lattice strips with fully periodic boundary conditions. / Chang, Shu-Chiuan; Shrock, Robert.

In: Physica A: Statistical Mechanics and its Applications, Vol. 292, No. 1-4, 15.03.2001, p. 307-345.

Research output: Contribution to journalArticle

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