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 γ=1 and ν=1/2 for Hamiltonian walks, along with
the exact value κ2=33/4 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.Comment: 12 pages, RevTeX, 3 figures supplied on request, ANU preprint
MRR-050-9