Lattice realizations of unitary minimal modular invariant partition functions

TL;DR

This paper numerically studies the conformal spectra of critical dilute A-D-E lattice models, showing they realize the A-D-E classification of unitary minimal modular invariant partition functions, with some models exhibiting factorization.

Contribution

It demonstrates that certain lattice models realize the complete A-D-E classification of modular invariant partition functions, providing numerical evidence for these realizations.

Findings

Models in branches 1 and 2 realize the A-D-E classification.

Models in branches 3 and 4 show factorization of partition functions.

Factorization also observed in two-color lattice models.

Abstract

The conformal spectra of the critical dilute A-D-E lattice models are studied numerically. The results strongly indicate that, in branches 1 and 2, these models provide realizations of the complete A-D-E classification of unitary minimal modular invariant partition functions given by Cappelli, Itzykson and Zuber. In branches 3 and 4 the results indicate that the modular invariant partition functions factorize. Similar factorization results are also obtained for two-colour lattice models.