Fluctuation effects in the herringbone orientational phase transition

We have studied the herringbone orientational transition of ${\mathrm{N}}_2$ molecules adsorbed on graphite, using two complementary approaches beyond mean field: a Kikuchi approximation and a real-space renormalization. In the latter the long-range fluctuations induced a first-order phase transition instead of the continuous one predicted in mean-field theory. The discontinuity fixed-point Hamiltonian keeps the coupling between the molecular and lattice orientations, being different from the q=6 Potts fixed point.