Abstract
In the present paper we continue the investigation from Bovier and Külske (1996 J. Stat. Phys. 83 751–59) and consider the SOS (solid-on-solid) model on the Cayley tree of order k ⩾ 2. In the ferromagnetic SOS case on the Cayley tree, we find three solutions to a class of period-4 height-periodic boundary law equations and these boundary laws define up to three periodic gradient Gibbs measures.
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