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Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs

Robert Shrock·Shan-Ho Tsai
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Abstract

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy $S_0$ for the $q$-state Potts antiferromagnet on families of cyclic and twisted cyclic (Möbius) strip graphs composed of $p$-sided polygons. Our results suggest a general rule concerning the maximal region in the complex $q$ plane to which one can analytically continue from the physical interval where $S_0 > 0$. The chromatic zeros and their accumulation set ${\cal B}$ exhibit the rather unusual property of including support for $Re(q) < 0$ and provide further evidence for a relevant conjecture.

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Robert Shrock, Shan-Ho Tsai. 1999-03-15. Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs. https://doi.org/10.1088/0305-4470%2F32%2F17%2F102

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