Phase transition in the n > 2 honeycomb O(n) model

We determine the phase diagram of the O(n) loop model on the honeycomb latt ice, in particular, in the range n > 2, by means of a transfer-matrix metho d. We find that, contrary to the prevailing expectation, there is a line of critical points in the range between n = 2 and infinity. This phase transi tion, which belongs to the three-state Potts universality class, is unphysi cal in terms of the O(n) spin model, but falls inside the physical region o f the n-component corner-cubic model. It can also be interpreted in terms o f the ordering of a system of soft particles with hexagonal symmetry.