Abstract
We determine the phase diagram of the O(n) loop model on the honeycomb lattice, in particular, in the range n>2, by means of a transfer-matrix method. 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 transition, which belongs to the three-state Potts universality class, is unphysical in terms of the O(n) spin model, but falls inside the physical region of the n-component corner-cubic model. It can also be interpreted in terms of the ordering of a system of soft particles with hexagonal symmetry.
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