1. An infinite-dimensional nonlinear equation related to Gibbs measures of a SOS model.
- Author
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Rozikov, U. A.
- Subjects
- *
NONLINEAR equations , *FUNCTIONAL equations , *DIFFERENCE equations , *NUMERICAL analysis , *GIBBS sampling , *VECTOR valued functions , *CAYLEY graphs - Abstract
For the solid-on-solid (SOS) model with an external field and with spin values from the set of all integers on a Cayley tree, each (gradient) Gibbs measure corresponds to a boundary law (an infinite-dimensional vector function defined on vertices of the Cayley tree) satisfying a nonlinear functional equation. Recently some translation-invariant and height-periodic (non-normalizable) solutions to the equation are found. Here, our aim is to find non-height-periodic and non-normalizable boundary laws for the SOS model. By such a solution one can construct a non-probability Gibbs measure. We find explicitly several non-normalizable boundary laws. Moreover, we reduce the problem to solving of a nonlinear, second-order difference equation. We give analytic and numerical analyses of the difference equation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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