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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

Shu-Chiuan Chang·Robert Shrock
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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 ${\cal B}$ 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 ${\cal B}$.

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Shu-Chiuan Chang, Robert Shrock. 2001-07-04. 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. https://doi.org/10.1103/physreve.64.066116

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