Fluctuation effect on the incommensurate transition of quartz

In the mean field description of the incommensurate transition of quartz, the triangular 3-q, the striped I-q and the fl phases meet at the same critical point. It is shown that critical fluctuations lift this degeneracy and transform the second order transition into first order ones. Furthermore, there is a regime of the parameter space where the I-q phase should appear between the fl and 3-q phases, even in the absence of any applied stress, as seen in recent experiments.