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arXiv · 1812.07744

Positive fixed points of cubic operators on $\mathbb{R}^{2}$ and Gibbs Measures

Yu. Kh. Eshkabilov·Sh. D. Nodirov
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Abstract

In this paper we consider one model with nearest-neighbor interactions and with the set $[0,1]$ of spin values on the Cayley tree of order three. Translation-invariant Gibbs measures for the model are studied. Results are proved by using properties of the positive fixed points of a cubic operator in the cone $\mathbb{R}_+^{2}$.

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Yu. Kh. Eshkabilov, Sh. D. Nodirov. 2018-12-19. Positive fixed points of cubic operators on $\mathbb{R}^{2}$ and Gibbs Measures. https://arxiv.org/abs/1812.07744

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