Intrinsic nanoscale inhomogeneity in ordering systems due to elastic-mediated interactions

Phase diagram and pattern formation in two-dimensional Ising model with coupling between order parameter and lattice vibrations is investigated by Monte-Carlo simulations. It is shown that if the coupling is strong enough (or phonons are soft enough) a short-range order exists in disordered phase for a broader temperature interval. Different types of this short-range order (stripe-like, checkboard-like, etc.) depending on the temperature and model parameters are investigated. With further increase of the coupling, a reconstruction of the ground state happens and new ordered phases appear at low enough temperatures.