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

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:
;
Publication Date:
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.
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
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.
@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}
}