Kac-Ward formula and its extension to order-disorder correlators through a graph zeta function

Michael Aizenman, Simone Warzel

Published 2017-09-18Version 1

A streamlined derivation of the Kac-Ward formula for the planar Ising model's partition function is presented and applied in relating the kernel of the Kac-Ward matrices' inverse with the correlation functions of the Ising model's order-disorder correlation functions. Used in the analysis is the formula's minor extension beyond planarity. A shortcut for both is enabled through the Bowen-Lanford graph zeta function relation.