Results 1 
5 of
5
Quantum Spin Systems at Positive Temperature
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 2007
"... We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar pha ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins S satisfy β ≪ √ S.Fromthe quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the BerezinLieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with S ≫ 1. The most notable examples are the quantum orbitalcompass model on Z 2 and the quantum 120degree model on Z 3 which are shown to exhibit symmetry breaking at lowtemperatures despite
Interfaces and droplets in quantum lattice models
 XIII International Congress of Mathematical Physics, A. Grigoryan, A. Fokas, T. Kibble, B. Zegarlinski (Eds), International
, 2001
"... ..."
Unspecified Book Proceedings Series
, 2000
"... Interfaces and droplets in quantum lattice models ..."
(Show Context)