Critical behaviour of the fully packed loop model on the square lattice

We investigate the critical behaviour of the fully packed O(n) loop model on the square lattice in which each vertex is visited once by a loop. A transfer-matrix analysis shows that this model can be interpreted as a superposition of a low-temperature O(n) model and an solid-on-solid (SOS) model, as for the fully packed model on the honeycomb lattice. However, not all of the critical exponents are the same for both lattices. In contrast, the fully packed model on the triangular lattice appears to behave as a pure low-temperature O(n) model.