A universal emulator for planar Ising lattices

Abstract

We introduce the notion of an Ising emulator for two-dimensional Ising models: flat, unit-edge-length lattices can be represented as site- or bond-diluted supercells of a single host lattice, for which the Feynman--Vdovichenko/Kac--Ward solution is fixed once and for all. We construct explicit square and triangular emulators and show that a single transition matrix, supplemented by lattice-specific binary masks, gives all the thermodynamic quantities of interest for both ferro- and antiferromagnetic couplings. We apply the framework to all eleven Archimedean lattices, to all twenty $2$-uniform lattices -- whose thermodynamics is obtained here for the first time -- and to several pentagonal lattices, and show that the same construction extends directly to fractal and disordered Ising models, with no modification to the underlying machinery.