Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-05-15
Phys. Rev. E62, 4650-4664 (2000)
Physics
Condensed Matter
Statistical Mechanics
39 pages, latex, 8 figures
Scientific paper
10.1103/PhysRevE.62.4650
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 $L_y=3$ and $L_y=4$ vertices and arbitrarily great length $L_x$ 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 2D lattice. These results give insight into the effect of such non-nearest 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 $L_x \to \infty$ limits of the strips that we study. With the generalization of $q$ from ${\mathbb Z}_+$ to ${\mathbb C}$, we determine the analytic structure of $W(q)$ in the $q$ plane for the various cases.
Chang Shu-Chiuan
Shrock Robert
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