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We studied the phase transitions and magnetic properties of the Ising model on a square lattice by the replica Monte Carlo method and by the method of transfer-matrix, the maximum eigenvalue of which was found by Lanczos method. The competing exchange interactions between nearest neighbors J 1 , second J 2 , third neighbors J 3 and an external magnetic field were taken into account. We found the frustration points and expressions for the frustration fields, at crossing of which cardinal changes of magnetic structures (translational invariance changes discontinuously) take place. A comparative analysis with 1D Ising model was performed and it was shown that the behavior of magnetic properties of the 1D model and the 2D model with J 1 and J 3 interactions reveals detailed similarity only distinguishing in scales of magnetic field and temperature.

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In part I of this series the problem of immanent chaotization of crystal structures was described in simple models and the mathematical approach to the calculation of diffuse scattering (DS) was described. It was formulated that the loose packing of most real crystals appears to be the universal microscopical cause of DS. In the present paper the microscopical nature of chaotization is analysed and a quantitative description of the structural loose packing is given for cubic perovskites; these are particularly convenient examples because the most vivid and thorough experimental data on DS were obtained for such crystals: KNbO3, BaTiO~, NaNbO3, KMnF3.