Exact Results for Hamiltonian Walks from the Solution of the Fully Packed Loop Model on the Honeycomb Lattice

TL;DR

This paper derives exact solutions for Hamiltonian walks on the honeycomb lattice using the fully packed loop model, revealing critical exponents and universality class distinctions.

Contribution

It provides the nested Bethe Ansatz solution for the fully packed O(n) loop model on the honeycomb lattice and extracts exact critical exponents for Hamiltonian walks.

Findings

Exact bulk free energy, central charge, and scaling dimensions derived.

Exact exponents for Hamiltonian walks: γ=1, ν=1/2.

Connective constant computed as κ^2 = 3√3/4.

Abstract

We derive the nested Bethe Ansatz solution of the fully packed O($n$) loop model on the honeycomb lattice. From this solution we derive the bulk free energy per site along with the central charge and geometric scaling dimensions describing the critical behaviour. In the $n=0$ limit we obtain the exact compact exponents $\gamma=1$ and $\nu=1/2$ for Hamiltonian walks, along with the exact value $\kappa^2 = 3 \sqrt 3 /4$ for the connective constant (entropy). Although having sets of scaling dimensions in common, our results indicate that Hamiltonian walks on the honeycomb and Manhattan lattices lie in different universality classes.