CMI Seminar: Alistair Sinclair
The Lee-Yang Theorem and the Ising Model
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.