### 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 L_{y} = 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 language | English |
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Pages (from-to) | 307-345 |

Number of pages | 39 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 292 |

Issue number | 1-4 |

DOIs | |

Publication status | Published - 2001 Mar 15 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics

### Cite this

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*Physica A: Statistical Mechanics and its Applications*, vol. 292, no. 1-4, pp. 307-345. https://doi.org/10.1016/S0378-4371(00)00544-6

**T = 0 partition functions for Potts antiferromagnets on lattice strips with fully periodic boundary conditions.** / Chang, Shu-Chiuan; Shrock, Robert.

Research output: Contribution to journal › Article

TY - JOUR

T1 - T = 0 partition functions for Potts antiferromagnets on lattice strips with fully periodic boundary conditions

AU - Chang, Shu-Chiuan

AU - Shrock, Robert

PY - 2001/3/15

Y1 - 2001/3/15

N2 - 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.

AB - 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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U2 - 10.1016/S0378-4371(00)00544-6

DO - 10.1016/S0378-4371(00)00544-6

M3 - Article

VL - 292

SP - 307

EP - 345

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-4

ER -