CMI Seminar: Alistair Sinclair

Tuesday May 7, 2019 4:00 PM

The Lee-Yang Theorem and the Ising Model

Speaker: Alistair Sinclair, UC Berkeley
Location: Annenberg 213

The celebrated Lee-Yang Theorem of the 1950s says that the zeros of the partition function of the ferromagnetic Ising model (viewed as a polynomial in the field parameter) lie on the unit circle in the complex plane. In this talk I will discuss a recent revival of interest in this result, inspired by computational questions. I will discuss three developments. First, I will explain how a generalization of the Lee-Yang theorem to rule out repeated zeros leads to hardness results for computing averages of observables associated with the Ising model. Then I will show how to combine the theorem with recent technology of Barvinok and others to obtain the first polynomial time deterministic approximation algorithms for the partition function. And finally I will discuss the relationship of the theorem to decay of correlations. The talk will be self-contained.

This is joint work with Jingcheng Liu and Piyush Srivastava.

Series Center for the Mathematics of Information (CMI) Seminar Series

Contact: Linda Taddeo at 626-395-6704 ltaddeo@caltech.edu
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