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SLE - non-local observables in critical systems

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Abstract: Domain walls in statistical systems are extended objects and hence by definition non-local. Since the models are defined by local Hamiltonians, typically containing only nearest neighbour interactions, providing a description of these domain walls is a non-trivial task. In this talk, I shall explain how a mathematical description of these curves has arisen at the critical point, based only on an interpretation of what is meant by the conformal invariance of the curves. This is known as Schramm Loewner evolution (SLE), predictions of which are seen to correspond to well-known correlation functions in conformal field theory. Some new results are presented: in particular, SLE is seen to be an adequate description of curves in the 3-state model with symmetry breaking boundary conditions, even though SLE is necessarily reflection symmetric.

This talk is part of the TCM Blackboard Series series.

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