Gibbs measures for the three-state SOS model with external field on a Cayley tree

被引：0
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作者：
Muzaffar M. Rahmatullaev
Obid Sh. Karshiboev
机构：
[1] Institute of Mathematics after named V.I. Romanovsky,Mathematics
[2] Chirchik State Pedagogical Institute of Tashkent Region,Mathematics
来源：
Positivity | 2022年 / 26卷
关键词：
Cayley tree; Gibbs measure; SOS model; External field; Primary 82B05; 82B20 Secondary 60K35; Primary 82B05; 82B20 Secondary 60K35;
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摘要：
We consider a three-state solid-on-solid (SOS) model in the presence of nonzero external field on a Cayley tree. We obtain a system of functional equations for this model, which each positive solution of the system corresponds to a splitting Gibbs measure. Using this, we study the translation-invariant splitting Gibbs measures (TISGMs) of the model. On the binary tree, we find all the TISGMs of the model.
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