Lace expansions and spin models

Abstract: I will review lace expansions starting with their relation to the other expansions in statistical mechanics and then discussing their application to spin models. Akira Sakai opened this avenue in 2007 with his proof that in sufficiently high dimension $d$ the two point function for the critical Ising model is asymptotic to $c_d |x-y|^{-(d-2)}$. In arxiv.org/abs/1905.09605 Tyler Helmuth, Mark Holmes and I have introduced a different way to derive lace expansions based on the Symanzik random walk representation.

mathematical physics

Audience: researchers in the discipline

( video )

One world IAMP mathematical physics seminar

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