Complex-Temperature Phase Diagrams for the q-State Potts Model on Self-Dual Families of Graphs and the Nature of the $q\to \infty$ Limit

Abstract

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on self-dual strip graphs $G$ of the square lattice with fixed width $L_y$ and arbitrarily great length $L_x$ with two types of boundary conditions. Letting $L_x\to \infty$, we compute the resultant free energy and complex-temperature phase diagram, including the locus $\mathcal{B}$ where the free energy is nonanalytic. Results are analyzed for widths $L_y=1,2,3$. We use these results to study the approach to the large-q limit of $\mathcal{B}$.

38 pages, latex, postscript figures included

References in corpus (3)

• Exact Potts Model Partition Functions on Wider Arbitrary-Length Strips of the Square Lattice
• Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q
• Potts Model Partition Functions for Self-Dual Families of Strip Graphs

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