Abstract
We present a number of exact results on the random-bond,q-state Potts model. The quenched model on any finite planar graph or lattice is shown to obey a duality relation for general type of bond-randomness. In the annealed case, the solution of the model reduces to that of the regular (nonrandom) Potts model on the corresponding lattice. Explicit knowledge of the critical parameters of theq-state Potts model in two dimensions allows us to evaluate exactly the phase diagram of the annealed model on the square, triangular and honeycomb lattices. We discuss the behavior near the (random) critical point and comment on the relationship between the quenched and annealed systems. The exact phase diagram of the annealed system is obtained for the bond-diluted model and the spin-glass model with and without dilutions.
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Work supported in part by NSF grant No. DMR-78-18808
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Sarbach, S., Wu, F.Y. Exact results on the random Potts model. Z. Physik B - Condensed Matter 44, 309–316 (1981). https://doi.org/10.1007/BF01294168
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DOI: https://doi.org/10.1007/BF01294168