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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
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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 Berezin-Lieb 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 orbital-compass model on Z 2 and the quantum 120-degree model on Z 3 which are shown to exhibit symmetry breaking at low-temperatures 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 ..."
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