On the nature of the phase transition in the three-dimensional random field Ising model

A brief survey of the theoretical, numerical and experimental studies of the random field Ising model (RFIM) during the last three decades is given. The nature of the phase transition in the three- dimensional RFIM with Gaussian random fields is discussed. Using simple scaling arguments it is shown that if the strength of the random fields is not too small ( bigger than a certain threshold value), the finite temperature phase transition in this system is equivalent to the low temperature order - disorder transition which takes place with variations of the strength of the random fields. A detailed study of the zero- temperature phase transition in terms of simple probabilistic arguments and a modified mean field approach ( which take into account nearest neighbor spin - spin correlations) is given. It is shown that if all thermally activated processes are suppressed, the ferromagnetic order parameter m( h) as a function of the strength h of the random fields becomes history dependent. In particular, the behavior of the magnetization curves m( h) for increasing and decreasing h reveals a hysteresis loop.