The influence of random interlayer exchange on the phase states of the simplest magnetic heterostructure consisting of two ferromagnetic Ising layers with large interaction radius is studied. It is shown that such system can exist in three magnetic phases: ferromagnetic, antiferromagnetic and ferrimagnetic. The possible phase diagrams and temperature dependencies of thermodynamic parameters are described. The regions of existence of the magnetic phases in external magnetic field are determined at zero temperature.PACS numbers: 64.60. Cn, 05.70.Jk, 64.60.Fr Thin films of layered magnets and artificial heterostructures composed of alternating magnetic and nonmagnetic layers can have a variety of stable magnetic states and switching between them can be achieved by different regimes of magnetic field variation 1,2,3 . This opens vast possibilities for numerous technical applications of such structures 4,5,6 and makes theoretical description of their magnetic states and properties of these states very actual. In particular, such description for finite number of layers can be achieved in some variants of mean-field approximations 6,7 or using numerical methods 8,9 , yet the study of ideal homogeneous systems can be insufficient for the description of experimental data. Indeed, impurities and defects in interlayer space modify generally the exchange constants, which could essentially transform magnetic state of layered structure. Fluctuations of nonmagnetic spacer thickness also give rise to the similar effect of local interlayer exchange modification 10,11 . Here we consider the influence of random interlayer exchange on the phase states of the simplest magnetic heterostructure consisting of two ferromagnetic Ising layers. It can be realized as thin two-layer crystal film having controlled concentration of impurities in the interlayer space or as two monoatomic layers deposited on the surfaces of nonmagnetic spacer with random thickness fluctuations. We consider the case when radius of intralayer ferromagnetic interaction is much larger than lattice parameter. Then the model can be treated in the mean-field approximation (except of narrow vicinity of transition point), i. e. the intralayer interaction radius can be put infinite. In such approximation it is quite easy to obtain the expression for averaged thermodynamic potential depending on the layers' magnetizations, establish possible magnetic phases of such system and describe its thermodynamic properties in these phases.
I. THERMODYNAMIC POTENTIAL OF RANDOM MAGNETIC BILAYERThe Hamiltonian of the model has the formHere S n,i = ±1 are Ising spins, index n numerates lattice cites in layers from 1 to N , i = 1, 2 is the layer number, J > 0 is the constant of intralayer ferromagnetic exchange,J n is random interlayer exchange, H is external magnetic field. We assume that allJ n have the common distribution functionIt describes the presence of impurities or defects of one sort with concentration p, which change the interlayer interaction constant on sites from J + in...