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Potts antiferromagnetic model on a family of fractal lattices: Exact results for an unusual phase.

The three-state antiferromagnetic Potts model on a family of bipartite diamond hierarchical lattices is investigated. This exactly solvable family of models exhibits a distinctive low-temperature phase of the type predicted by Berker and Kadanoff for complex systems with a macroscopically degenerate ground state. An analytic expression for the residual entropy is derived. We prove that there are some similarities between this phase and that of Kosterlitz-Thouless, namely, the power-law decay of correlations, the vanishing of the order parameter, and the absence of divergence in the specific heat. It is also shown that the local order parameter has two distinct multifractal structures: one at the critical point and another at the unusual phase.