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

## TL;DR

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## Contribution

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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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Source: https://tomesphere.com/paper/1812.07744