2 research outputs found
On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three
In the present paper we study forward Quantum Markov Chains (QMC) defined on
a Cayley tree. Using the tree structure of graphs, we give a construction of
quantum Markov chains on a Cayley tree. By means of such constructions we prove
the existence of a phase transition for the XY-model on a Cayley tree of order
three in QMC scheme. By the phase transition we mean the existence of two now
quasi equivalent QMC for the given family of interaction operators
.Comment: 34 pages, 1 figur
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 different
(where is the number of ground states) Gibbs measures.Comment: 12 page