Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2007-06-05
Physics
Condensed Matter
Disordered Systems and Neural Networks
22 pages, 12 figures
Scientific paper
10.1088/1742-5468/2007/09/P09005
A brief survey of the theoretical, numerical and experimental studies of the random field Ising model during last three decades is given. 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 at variations of the strength of the random fields. Detailed study of the zero-temperature phase transition in terms of simple probabilistic arguments and modified mean-field approach (which take into account nearest-neighbors spin-spin correlations) is given. It is shown that if all thermally activated processes are suppressed the ferromagnetic order parameter m(h) as the 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 for decreasing $h$ reveals the hysteresis loop.
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