Phase transitions for a model with uncountable set of spin values on a Cayley tree
Yu. Kh. ÈshkabilovFaculty of Mechanics and Mathematics National University of Uzbekistan, Tashkent, UzbekistanU. A. RozikovInstitute of Mathematics, National University of Uzbekistan, Tashkent, UzbekistanG. I. BotirovFaculty of Physics and Mathematics of Bukhara State University, Bukhara, Uzbekistan
ABI
Аннотация
In this paper we consider a model with nearest-neighbor interactions and with the set [0, 1] of spin values, on a Cayley tree of order k ≥ 2. To study translation-invariant Gibbs measures of the model we drive an nonlinear functional equation. For k = 2 and 3 under some conditions on parameters of the model we prove non-uniqueness of translation-invariant Gibbs measures (i.e., there are phase transitions).
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