On the construction of integrable dilute ADE models

TL;DR

This paper introduces an integrable extension of lattice models based on connected graphs, linking them to dilute ADE models and conjecturing their critical regimes as dilute SOS models of ADE type.

Contribution

It presents a new class of IRF lattice models with spins on arbitrary connected graphs, extending previous models and conjecturing their critical behavior as dilute ADE SOS models.

Findings

Models are IRF with spins on connected graphs

Underlying vertex model is the Izergin-Korepin model

Conjecture: critical regimes correspond to dilute ADE SOS models

Abstract

We give an integrable extension of the lattice models recently considered by I.Kostov in his study of strings in discrete space. These models are IRF models with spin variables living in any connected graph, the vertex model underlying these models is the Izergin-Korepin model. When the graph is taken to be a simply laced Dynkin diagram, it is conjectured that these models possess critical regimes which are the dilute phase of SOS models of ADE type.