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The European Physical Journal B

Ground-state entropy of Ising antiferromagnets with general spinS

Dragan Slavkov Hajdukovic, Ilija M. Savić, Lj. Damjanović

Published Sep 1, 1984• 7 citations
Publisher
DOI
10.1007/bf01318414

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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 Lx 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 Lx-->infinity limits of the strips that we study. With the generalization of q from Z+ to C, we determine the analytic structure of W(q) in the q plane for the various cases.
The ground state entropy density of the triangular Ising antiferromagnet is considered as a function of boundary conditions on domains for which the ground states do not admit a dimer covering. These domains admit a rich set of ground states that cannot be classified in the usual way in terms of nonintersecting strings. Various parametrized boundary conditions and domain shapes are identified that allow the ground state entropy density to be varied between zero and maximal degeneracy. The dependence of degeneracy on boundary spins and/or domain shape is interpreted in terms of strings that are not restricted to be nonintersecting.