# Mirror Symmetry of Height-Periodic Gradient Gibbs Measures of an SOS Model on Cayley Trees

@article{Rozikov2022MirrorSO, title={Mirror Symmetry of Height-Periodic Gradient Gibbs Measures of an SOS Model on Cayley Trees}, author={Utkir A. Rozikov}, journal={Journal of Statistical Physics}, year={2022} }

. For the solid-on-solid (SOS) model with spin values from the set of all integers on a Cayley tree we give gradient Gibbs measures (GGMs). Such a measure corresponds to a boundary law (which is an inﬁnite-dimensional vector-valued function deﬁned on vertices of the Cayley tree) satisfying an inﬁnite system of functional equations. We give several concrete GGMs of boundary laws which are independent from vertices of the Cayley tree and (as an inﬁnite-dimensional vector) have periodic, (non…

## 3 Citations

### A non-linear second-order difference equation related to Gibbs measures of a SOS model

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- 2022

. For the SOS (solid-on-solid) model with an external ﬁeld and with spin values from the set of all integers on a Cayley tree each (gradient) Gibbs measure corre-sponds to a boundary law (an…

### Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees

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. The work is devoted to gradient Gibbs measures (GGMs) of a SOS model with countable set Z of spin values and having alternating magnetism on Cayley trees. This model is deﬁned by a nearest-neighbor…

### Fixed points of an infinite dimensional operator related to Gibbs measures

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. We describe ﬁxed points of an inﬁnite dimensional non-linear operator related to a hard core (HC) model with a countable set N of spin values on the Cayley tree. This operator is deﬁned by a…

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