On a sub-wavelength scale, atoms in a crystal, i. e. an ordered lattice, are normally assumed to be almost uniformly excited by an incident light. An interatomic interaction produces then a uniform local field (different from that of incident laser) at each atom as well. This is a major assumption in the Lorentz-Lorenz theory of interaction of light with dense matter. We showed  that at certain critical conditions on the atomic density and dipole strength, a previously unexpected phenomenon emerges: the interacting atoms break the uniformity of interaction, and in a violent switch to a strong non-uniformity, their excitation and local field form nanoscale strata with a spatial period much shorter than that of laser wavelength, thus changing the entire paradigm of light-matter interaction. The most interesting effects can be observed for relatively small 1D-arrays or 2D lattices if the laser is almost resonant to an atomic quantum transition. The effects include huge local field enhancement at size-related resonances at the frequencies near the atomic line, so that the strata are readily controlled by laser tuning. A striking feature is that for the shortest strata, the nearest atomic dipoles counter-oscillate, which is reminiscent of anti-ferromagnetism of magnetic dipoles in Ising model.