Characterizing partition functions of the spin model by rank growth

TL;DR

This paper characterizes which graph invariants can be represented as partition functions of spin models over complex numbers, using the concept of rank growth of connection matrices.

Contribution

It introduces a new characterization of spin model partition functions based on the rank growth of associated connection matrices.

Findings

Identifies conditions for graph invariants to be spin model partition functions.

Uses rank growth of connection matrices as a key criterion.

Provides a framework for analyzing spin models through algebraic invariants.

Abstract

We characterize which graph invariants are partition functions of a spin model over the complex numbers, in terms of the rank growth of associated `connection matrices'.