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

TL;DR

This paper reviews the phase transition characteristics of the three-dimensional random field Ising model, highlighting the equivalence of finite temperature and low-temperature transitions under certain conditions, and discusses zero-temperature transition behavior including hysteresis effects.

Contribution

It provides a detailed analysis of the phase transition nature in the 3D RFIM using scaling, probabilistic, and mean-field approaches, emphasizing the role of random field strength and history dependence.

Findings

Finite temperature transition is equivalent to low-temperature order-disorder transition for sufficiently strong random fields.

Zero-temperature transition exhibits hysteresis in magnetization curves.

Order parameter behavior depends on the history of the random field strength.

Abstract

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.