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

Journal Article · Sun Oct 01 04:00:00 EDT 2000 · Physical Review E

DOI:https://doi.org/10.1103/PhysRevE.62.4650· OSTI ID:40205393

Chang, Shu-Chiuan; Shrock, Robert

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.

• Sponsoring Organization: (US)
• OSTI ID: 40205393
• Journal Information: Physical Review E, Journal Name: Physical Review E Journal Issue: 4 Vol. 62; ISSN 1063-651X
• Publisher: The American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
ENTROPY
PARTITION FUNCTIONS