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The Phase Diagram of the Quantum Curie-Weiss Model |
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| Authors: | Lincoln Chayes Nicholas Crawford Dmitry Ioffe Anna Levit |
| Affiliation: | (1) Department of Mathematics, University of California at Los Angeles, Los Angeles, USA;(2) Department of Statistics, University of California at Berkeley, Berkeley, USA;(3) Department of Industrial Engineering, The Technion, Haifa, Israel |
| Abstract: | This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model, we give a complete picture of the phase diagram of the model in the parameters of inverse temperature and transverse field strength. Further analysis computes the critical exponent for the vanishing of the order parameter in the approach to the critical curve and gives useful stability properties for a variational problem associated with the representation. |
| Keywords: | Quantum spin systems Phase diagrams Mean field theory Large deviations Random current representation Ising model Feynman-Kac transformation |
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