Operator Spectrum and Exact Exponents of the Fully Packed Loop Model

TL;DR

This paper develops a Coulomb gas framework for the fully packed loop model on the honeycomb lattice, providing exact operator spectra, scaling dimensions, and geometric properties like fractal dimension and loop size distribution.

Contribution

It introduces a complete operator spectrum in terms of electric and magnetic charges and computes their scaling dimensions exactly, advancing understanding of the model's critical behavior.

Findings

Exact scaling dimensions of operators are derived.

Fractal dimension of loops is calculated.

Loop size distribution function is obtained.

Abstract

We develop a Coulomb gas description of the critical fluctuations in the fully packed loop model on the honeycomb lattice. We identify the complete operator spectrum of this model in terms of electric and magnetic {\em vector}-charges, and we calculate the scaling dimensions of these operators exactly. We also study the geometrical properties of loops in this model, and we derive exact results for the fractal dimension and the loop size distribution function. A review of the many different representations of this model that have recently appeared in the literature, is given.