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Stochastic geometry of the quantum Ising model

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The classical Ising model is a well-studied model for phase transition. A particularly fruitful way to study this model is via its `graphical representations’, which allow us to use ideas and arguments from stochastic geometry and percolation theory. This talk will focus on graphical representations of the QUANTUM Ising model, a much less studied topic. In joint work with Geoffrey Grimmett, we were able to use graphical representations to deduce fundamental facts about the quantum Ising model. Most notable of these are sharpness of the phase transition in all dimensions, and bounds on some critical exponents.

This talk is part of the Probability series.

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