Ground States and Gibbs Measures for the Potts-SOS Model with an External Field on the Cayley Tree

We consider the Potts-SOS model with non-zero external field on the Cayley tree. We describe the ground states for the Potts-SOS model with a translation-invariant external field. We verify the Peierls condition for the model. Using a contour argument, we show the existence of two different Gibbs measures at sufficiently low temperatures. Periodic ground states for the Potts-SOS model with a periodic external field are also found.

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