Exact Partition Functions for Potts Antiferromagnets on Cyclic Lattice Strips

Details Exact Partition Functions for Potts Antiferromagnets on Cyclic Lattice Strips Exact Partition Functions for Potts Antiferromagnets on Cyclic Lattice Strips

1999-07-26

arxiv.org/abs/cond-mat/9907403v1

Physica A275, 429-449 (2000)

Physics

Condensed Matter

Statistical Mechanics

27 pages, Latex, 4 postscript figures, Physica A, in press

Scientific paper

We present exact calculations of the zero-temperature partition function of the $q$-state Potts antiferromagnet on arbitrarily long strips of the square, triangular, and kagom\'e lattices with width $L_y=2$ or 3 vertices and with periodic longitudinal boundary conditions. From these, in the limit of infinite length, we obtain the exact ground-state entropy $S_0=k_B \ln W$. These results are of interest since this model exhibits nonzero ground state entropy $S_0 > 0$ for sufficiently large $q$ and hence is an exception to the third law of thermodynamics. We also include results for homeomorphic expansions of the square lattice strip. The analytic properties of $W(q)$ are determined and related to zeros of the chromatic polynomial for long finite strips.

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