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

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.

Nonequilibrium phase transitions and tricriticality in a three-dimensional lattice system with random-field competing kinetics

“…For the numerical implementation, the algorithm is as follows: at each time step, a new configuration of random fields {h} is generated according to P (h), Eq. (2); then, every lattice site is visited, and a spin flip occurs according to rate (3). In other words, the random variables h vary with time, i.e., the system is described at each time by Eq.…”

“…The Random Field Ising Model (RFIM) is one of the most studied systems in magnetism (for reviews, see [1,2] and more recently [3]), because of its mathematical simplicity and because the possibility of reproducting frustration, a phenomenon that occurs in real magnetic systems. In addition, the identification of the RFIM with some diluted antiferromagnets in * Electronic address: nuno@if.uff.br the presence of a uniform magnetic field [4,5], like Fe x Zn 1−x F 2 and Fe x Mg 1−x Cl 2 [2,6,7], have attracted the attention of theoretical and experimental researchers.…”

Phase diagram of the 3D bimodal random-field Ising model

“…This applies also for the bimodal RFIM, for which, with the exception of the estimation of h c from ground-state calculations [28,29,30], a reliable approximation of the phase diagram is still lacking. Furthermore, despite the 30 years of theoretical and experimental study the nature and scaling features of the transition of the RFIM are not yet well understood [38,39,40]. Nowadays, it is generally believed that the transition from the ordered to the disordered phase is continuous, governed by the zero-temperature random fixed-point [7,9,11], but a complete set of values of the critical exponents fulfilling scaling relations has not been established, despite the fact that several bounds [41] and further inequalities [8,42] for the critical exponents have been proposed, together with modified scaling relations [43].…”

Spin-1 Hopfield model under a random field

“…The thermodynamic properties introduced by RFs have remained controversial for more than 30 years (for a recent review in the RFIM see e.g. [4,[7][8][9]). For instance, several studies display broad divergences even for the RFIM phase diagram structure [4,[7][8][9].…”

“…[4,[7][8][9]). For instance, several studies display broad divergences even for the RFIM phase diagram structure [4,[7][8][9]. On the other hand, the effect of RFs on the SG phase has also been investigated [10][11][12][13][14].…”