A Contour Method on Cayley tree

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of $s$ different (where $s$ is the number of ground states) Gibbs measures.Comment: 12 page

l-Volterra Quadratic Stochastic Operators: Lyapunov Functions, Trajectories

We consider `-Volterra quadratic stochastic operators defined on (m? 1)-dimensional simplex, where ` 2 f0; 1; :::;mg. Under some conditions on coefficients of such operators we describe Lyapunov functions and apply them to obtain upper estimates for the set of !- limit points of trajectories. We describe a set of fixed points of `-Volterra operators

On Four State Hard Core Models on the Cayley Tree

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