| Description |
This is going to be an informal seminar on a current work in progress on the possibility of studying the Ising model using non-local fields on the complex plane. The mapping applies to more general models but we discuss the O(1) for simplicity. We introduce an exact mapping between fields indexed in N with functions on the complex plane - which does not require a continuous limit. The binary character of the Ising model is enforced via an interaction with an auxiliary field whose coupling is the temperature. This is going to be a whiteboard talk, and we focus in particular where to go from here, and the drawbacks and the advantages of using this approach. We show in particular the connection to a U(1) Group Field Theory, a certain parameter scaling limit for the perturbation theory, and end with a discussion on future work: the connection to random matrix theory for the study of glasses in this limit and discuss the constructive approach for this theory.
Based on: https://arxiv.org/abs/1908.08065 |
Joint ICTP/SISSA Statistical Physics Seminar: Continuum Field Theory for the Ising Model
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