Loop models and their critical points

TL;DR

This paper introduces new loop models with critical points characterized by conformal field theories, expanding the understanding of their phase transitions and mathematical structure.

Contribution

The paper presents novel loop models, including fully-packed and dilute types, with critical points described by superconformal minimal models and SU(2)_k WZW models, broadening the theoretical framework.

Findings

Critical points described by conformal field theories.

Extension to SU(2)_k models in dilute loop models.

New models unify various known loop models.

Abstract

Loop models have been widely studied in physics and mathematics, in problems ranging from polymers to topological quantum computation to Schramm-Loewner evolution. I present new loop models which have critical points described by conformal field theories. Examples include both fully-packed and dilute loop models with critical points described by the superconformal minimal models and the SU(2)_2 WZW models. The dilute loop models are generalized to include SU(2)_k models as well.