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

Abstract

A brief survey of the theoretical, numerical and experimental studies of the random fieldIsing model (RFIM) during the last three decades is given. The nature of the phasetransition in the three-dimensional RFIM with Gaussian random fields is discussed. Usingsimple scaling arguments it is shown that if the strength of the random fields is nottoo small (bigger than a certain threshold value), the finite temperature phasetransition in this system is equivalent to the low temperature order–disordertransition which takes place with variations of the strength of the random fields.A detailed study of the zero-temperature phase transition in terms of simpleprobabilistic arguments and a modified mean field approach (which take intoaccount nearest neighbor spin–spin correlations) is given. It is shown that if allthermally activated processes are suppressed, the ferromagnetic order parameterm(h) as a functionof the strength h of the random fields becomes history dependent. In particular, the behavior of the magnetization curvesm(h) for increasingand decreasing h reveals a hysteresis loop.