Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs

Details Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs

1999-05-30

arxiv.org/abs/cond-mat/9905431v1

J. Phys. A32 (1999) 5053-5070

Physics

Condensed Matter

Statistical Mechanics

27 pages, Latex, 17 figs. J. Phys. A, in press

Scientific paper

10.1088/0305-4470/32/27/306

We present exact calculations of chromatic polynomials for families of cyclic graphs consisting of linked polygons, where the polygons may be adjacent or separated by a given number of bonds. From these we calculate the (exponential of the) ground state entropy, $W$, for the q-state Potts model on these graphs in the limit of infinitely many vertices. A number of properties are proved concerning the continuous locus, ${\cal B}$, of nonanalyticities in $W$. Our results provide further evidence for a general rule concerning the maximal region in the complex q plane to which one can analytically continue from the physical interval where $S_0 > 0$.

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