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Summerschool on "Current Topics in Mathematical Physics"
Organizers: Maria Esteban (Paris Dauphine), Mathieu Lewin (Cergy) & Robert Seiringer (Vienna)


Daniel Ueltschi (Warwick, UK): "Quantum spin systems and phase transitions" 1
Monday 02 September 2013, 09:30 - 10:30
CIRM Marseille


Abstract: These lectures will be an introduction to the quantum Heisenberg model and other related systems. We will review the Hilbert space, the spin operators, the Hamiltonian, and the free energy. We will restrict ourselves to equilibrium systems. The main questions deal with the nature of equilibrium states and the phase transitions. We will review some of the main results such as the Mermin-Wagner theorem and the method of reflection positivity, that allows to prove the existence of phase transitions. Finally, we will discuss certain probabilistic representations and their consequences.