Square to hexagonal lattice transition in a vortex system

We study the vortex ordering as a function of the distance to a surface in which a square structure is imposed by surface pinning. The applied magnetic field is perpendicular to the surface and matches the concentration of pinning centers. Our model allows us to follow continuously the square to hexagonal group-non-subgroup transformation for a case in which macroscopic movements of the involved particles are not allowed. We find that the transition involves correlated movements of the particles inside large supercells. Several possible supercells are constructed by geometrical considerations. Comparison with recent experiments suggests that some of the measured structures are metastable.