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

Phase diagram and pattern formation in a two-dimensional Ising model with coupling between order parameter and lattice vibrations are 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 the disordered phase for a broader temperature interval. Different types of this short-range order (stripe-like, chessboard-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