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arXiv:cond-mat/9608095 · Journal of Physics A Mathematical and General

Ground state entropy and theq= 3 Potts antiferromagnet on the honeycomb lattice

Robert E. Shrock, Shan-Ho Tsai

Published Jan 21, 1997• 43 citations
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Abstract

We study the q-state Potts antiferromagnet with q=3 on the honeycomb lattice. Using an analytic argument together with a Monte Carlo simulation, we conclude that this model is disordered for all . We also calculate the ground state entropy to be and discuss this result.
DOI
10.1088/0305-4470/30/2/015

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The phase diagram of the q=3q=3q=3 state Potts antiferromagnet in a field is studied by exact mappings and Monte Carlo methods, and it is shown that systems with macroscopic ground-state degeneracy may exhibit conventional-type critical ordering. Our Monte Carlo data for the square-lattice case indicate a finite-temperature ordering in a range of field values where the entropy of the ground state is extensive. In a particular limit this phase transition can be shown to be of the Ising type by mapping the Potts model onto a colored, nearest-neighbor exclusion lattice gas. We also discuss the phase diagram of the body-centered-cubic Ising antiferromagnet in a field in order to show that renormalization-group arguments alone are not sufficient to restrict the diversity of possible low-temperature phases occurring in systems with a macroscopically degenerate ground state.
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