Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice

doi:https://doi.org/10.1103/PhysRevE.62.4650

Title: Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice

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Abstract

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and W(q), the exponent of the ground-state entropy, for the q-state Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on square lattice strips, of width L{sub y}=3 and L{sub y}=4 vertices and arbitrarily great length L{sub x} vertices, with both free and periodic boundary conditions. The resultant values of W for a range of physical q values are compared with each other and with the values for the full two-dimensional lattice. These results give insight into the effect of such nonnearest-neighbor couplings on the ground-state entropy. We show that the q=2 (Ising) and q=4 Potts antiferromagnets have zero-temperature critical points on the L{sub x}{yields}{infinity} limits of the strips that we study. With the generalization of q from Z{sub +} to C, we determine the analytic structure of W(q) in the q plane for the various cases.

Authors:: Chang, Shu-Chiuan; Shrock, Robert

Publication Date:: 2000-10-01

Sponsoring Org.:: (US)

OSTI Identifier:: 40205393

Resource Type:: Journal Article

Journal Name:: Physical Review E

Additional Journal Information:: Journal Volume: 62; Journal Issue: 4; Other Information: Othernumber: PLEEE8000062000004004650000001; 034010PRE; PBD: Oct 2000; Journal ID: ISSN 1063-651X

Publisher:: The American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; ENTROPY; PARTITION FUNCTIONS

Citation Formats


                    Chang, Shu-Chiuan, and Shrock, Robert. Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice.  United States: N. p., 2000. 
        Web.  doi:10.1103/PhysRevE.62.4650.

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                    Chang, Shu-Chiuan, & Shrock, Robert. Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice.  United States.  https://doi.org/10.1103/PhysRevE.62.4650

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                    Chang, Shu-Chiuan, and Shrock, Robert. Sun .  
        "Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice".  United States.  https://doi.org/10.1103/PhysRevE.62.4650.

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@article{osti_40205393,

  title        = {Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice},

  author       = {Chang, Shu-Chiuan and Shrock, Robert},

  abstractNote = {We present exact calculations of the zero-temperature partition function (chromatic polynomial) and W(q), the exponent of the ground-state entropy, for the q-state Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on square lattice strips, of width L{sub y}=3 and L{sub y}=4 vertices and arbitrarily great length L{sub x} vertices, with both free and periodic boundary conditions. The resultant values of W for a range of physical q values are compared with each other and with the values for the full two-dimensional lattice. These results give insight into the effect of such nonnearest-neighbor couplings on the ground-state entropy. We show that the q=2 (Ising) and q=4 Potts antiferromagnets have zero-temperature critical points on the L{sub x}{yields}{infinity} limits of the strips that we study. With the generalization of q from Z{sub +} to C, we determine the analytic structure of W(q) in the q plane for the various cases.},

  doi          = {10.1103/PhysRevE.62.4650},

  url          = {https://www.osti.gov/biblio/40205393},
  journal      = {Physical Review E},

  issn         = {1063-651X},

  number       = 4,

  volume       = 62,

  place        = {United States},

  year         = {2000},

  month        = {10}

}

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