Quasi-one-dimensional Ising models with defects of the “random local field” type: the Imry–Ma phase in spaces with a dimension higher than the lower critical dimensionality

The “temperature–defect concentration” phase diagram of quasi-one-dimensional Ising models with defects of the “random local field” type is studied. The competition of the tendency to the formation of a long-range order due to a weak interaction between one-dimensional spin chains and the tendency to the formation of the Imry–Ma phase in which the order parameter follows fluctuations of a random field induced by defects is studied too. The formation of the Imry–Ma phase is shown to be possible in the situation as the space dimension is higher than the lower critical dimension. The problem of the existence a long-range order in the Ising model with random fields is considered in a space with critical dimension $d_l$ = 2.