Potts critical frontiers of inhomogeneous and asymmetric bow-tie lattices

TL;DR

This paper derives exact critical frontiers for the Potts model on inhomogeneous and asymmetric bow-tie lattices by decomposing complex lattices into triangular cells, expanding the class of solvable models.

Contribution

It introduces a method to find exact critical points on more general inhomogeneous lattices, including 4-uniform and asymmetric bow-tie lattices, using lattice decomposition techniques.

Findings

Exact critical frontiers for various inhomogeneous bow-tie lattices

Critical points for asymmetric bow-tie lattices

Extension of solvable models to more complex lattice structures

Abstract

We study the critical frontiers of the Potts model on two-dimensional bow-tie lattices with fully inhomogeneous coupling constants. Generally, for the Potts critical frontier to be found exactly, the underlying lattice must be a 3-uniform hypergraph. A more general class of lattices are the 4-uniform ones, with unit cells contained within four boundary vertices. We demonstrate that in some cases, such lattices can be decomposed into triangular cells, and solved using a modification of standard techniques. This leads to the exact inhomogeneous Potts critical frontiers on various lattices, such as the bow-tie lattice with five different couplings, and critical points for asymmetric bow-tie lattices.