Phase transitions for quantum Markov chains associated with ising type models on a Cayley tree

Mukhamedov, Farrukh and Barhoumi, Abdessatar and Souissi, Abdessatar (2016) Phase transitions for quantum Markov chains associated with ising type models on a Cayley tree. Journal of Statistical Physics, 163 (3). pp. 544-567. ISSN 0022-4715 E-ISSN 1572-9613 (In Press)

PDF - Published Version Restricted to Repository staff only Download (444kB) | Request a copy

Abstract

The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper, we provide a more general construction of forward QMC. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states the existence of a phase transition for the Ising model with competing interactions on aCayley tree of order two. By the phase transition we mean the existence of two distinct QMC which are not quasi-equivalent and their supports do not overlap. We also study some algebraic property of the disordered phase of the model, which is a new phenomena even in a classical setting.

Item Type:	Article (Journal)
Additional Information:	5537/50295
Uncontrolled Keywords:	Quantum Markov chain · Cayley tree · Ising type model · Competing interaction · Phase transition · Quasi-equivalence · Disordered phase
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	25 Apr 2016 14:12
Last Modified:	06 Jan 2017 08:29
URI:	http://irep.iium.edu.my/id/eprint/50295

Actions (login required)

View Item