Ground states for the SOS model with an external field on the Cayley tree

We consider a nearest-neighbor solid-on-solid (SOS) model, with several spin values 0, 1, 2, ..., m, m ≥ 2 and non zero external field, on a Cayley tree of order k.In the case k = 2, m = 2, we describe translation-invariant ground states for the SOS model with a translation-invariant external field.Some periodic ground states for the SOS model with periodic external field are described.

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