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Random loop models and quantum spin systems

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The random loop representations of quantum Heisenberg models allow to study these systems using probabilistic methods. They were introduced twenty years ago by Toth and Aizenman-Nachtergaele. I will review rigorous results and open questions. I will describe a probabilistic proof of exponential decay of transverse quantum correlations (joint work with J. Bjornberg).

This talk is part of the Probability series.

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