Mesoscopic disorder in double-well optical lattices

Double-well optical lattices are considered, each cite of which is formed by a double-well potential. The lattice is assumed to be in an insulating state and order and disorder are defined with respect to the displacement of atoms inside the double-well potential. It is shown that in such lattices, in addition to purely ordered and disordered states, there, can exist an intermediate mixed state, where, inside a generally ordered lattice, there appear disordered regions of mesoscopic size.