$C$-networks and the planar Ising inverse problem

Abstract

We solve the inverse problem for Ising models on reduced planar graphs in a disk, i.e., recovering the edge coupling constants from the boundary spin correlations. A recursive solution to this problem was provided by Galashin--Pylyavskyy. Our solution is non-recursive. It is based on an Ising analog of the chamber ansatz which asserts that the inverse map should factor through variables on the graph that transform under the Ising Y-$\hat{I}”$ move according to the discrete CKP equation.

34 pages, 19 figures. Comments are welcome!