Correlation Length and Average Loop Length of the Fully-Packed Loop Model

TL;DR

This paper investigates the fully-packed loop model on a honeycomb lattice, deriving explicit formulas for correlation length and average loop length using integrable lattice model techniques and Bethe ansatz solutions.

Contribution

It introduces a perturbative formalism to verify known results and provides explicit expressions for key physical quantities in the many-loop phase.

Findings

Explicit formulas for correlation length and average loop length

Verification of results using perturbative formalism

Comparison with surface tension results

Abstract

The fully-packed loop model of closed paths covering the honeycomb lattice is studied through its identification with the $sl_q(3)$ integrable lattice model. Some known results from the Bethe ansatz solution of this model are reviewed. The free energy, correlation length, and the ensemble average loop length are given explicitly for the many-loop phase. The results are compared with the known result for the model's surface tension. A perturbative formalism is introduced and used to verify results.