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

Abstract

We consider a nearest-neighbor solid-on-solid (SOS) model, with several spin values $0,1,2,...,m, m\geq2$ 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.