Partition Function Zeros of a Restricted Potts Model on Self-Dual Strips of the Square Lattice

Details Partition Function Zeros of a Restricted Potts Model on Self-Dual Strips of the Square Lattice Partition Function Zeros of a Restricted Potts Model on Self-Dual Strips of the Square Lattice

2006-02-07

arxiv.org/abs/cond-mat/0602178v1

Int. J. Mod. Phys. B21, 1755-1773 (2007)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 6 figures

Scientific paper

10.1142/S021797920703703X

We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for self-dual cyclic square-lattice strips of various widths $L_y$ and arbitrarily great lengths $L_x$, with $Q$ and $v$ restricted to satisfy the relation $Q=v^2$. From these calculations, in the limit $L_x \to \infty$, we determine the continuous accumulation locus ${\cal B}$ of the partition function zeros in the $v$ and $Q$ planes. A number of interesting features of this locus are discussed and a conjecture is given for properties applicable for arbitrarily great width. Relations with the loci ${\cal B}$ for general $Q$ and $v$ are analyzed.

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