Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice |
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Authors: | Shu-Chiuan Chang Robert Shrock |
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Institution: | (1) Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan;(2) Physics Division, National Center for Theoretical Science, National Taiwan University, Taipei, 10617, Taiwan;(3) C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, NY 11794-3840, USA |
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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 strip graphs G of the honeycomb lattice for a variety of transverse widths equal to L
y
vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary
conditions. These partition functions have the form
, where m denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for N
Z,G,j
for arbitrary L
y
. We also present plots of zeros of the partition function in the q plane for various values of v and in the v plane for various values of q. Plots of specific heat for infinite-length strips are also presented, and, in particular, the behavior of the Potts antiferromagnet
at
is investigated. |
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Keywords: | Potts model Honeycomb lattice Exact solutions Transfer matrix |
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