Multicritical behavior in a random-field Ising model under a continuous-field probability distribution

Abstract

A random-field Ising model that is capable of exhibiting a rich variety of multicritical phenomena, as well as a smearing of such behavior, is investigated. The model consists of an infinite-range-interaction Ising ferromagnet in the presence of a triple Gaussian random magnetic field, which is defined as a superposition of three Gaussian distributions with the same width σ, centered at H = 0 and H = ± H(0), with probabilities p and (1-p)/2, respectively. Such a distribution is very general and recovers, as limiting cases, the trimodal, bimodal and Gaussian probability distributions. In particular, the special case of the random-field Ising model in the presence of a trimodal probability distribution (limit [Formula: see text]) is able to present a rather nontrivial multicritical behavior. It is argued that the triple Gaussian probability distribution is appropriate for a physical description of some diluted antiferromagnets in the presence of a uniform external field, for which the corresponding physical realization consists of an Ising ferromagnet under random fields whose distribution appears to be well represented in terms of a superposition of two parts, namely a trimodal and a continuous contribution. The model is investigated by means of the replica method, and phase diagrams are obtained within the replica-symmetric solution, which is known to be stable for the present system. A rich variety of phase diagrams is presented, with one or two distinct ferromagnetic phases, continuous and first-order transition lines, tricritical, fourth-order, critical end points and many other interesting multicritical phenomena. Additionally, the present model carries the possibility of destroying such multicritical phenomena due to an increase in the randomness, i.e. increasing σ, which represents a very common feature in real systems.

The random-field Ising model with asymmetric bimodal probability distribution

“…[41]; however, in order to describe these points (except the first two) the considered expansion of the free energy (11) has to be extended to higher-order terms [10,37,42,43] so that the criteria for such a point are satisfied, but this is beyond the scope of the current research.…”

“…(36), whereas group-2 includes again the zero-solution and the nonzero ones M 2 , M 3 , M 4 of Eq. (37). Depending on the value of p and h 0 , there can be transitions between these two groups.…”

“…The SOPT boundary is determined by setting A = 1 and C < 0, whereas for the FOPT boundary by A = 1 and C > 0 [6-9,12,18,23]. These two boundaries, whenever they coexist, are joined at a tricritical point determined by the condition A = 1 and C = 0 [6][7][8][9]12,36,37,18,23], provided that E < 0 (equivalently, F 6 < 0) as in Refs. [36,37].…”

Effects of the randomly distributed magnetic field on the phase diagrams of Ising nanowire I: Discrete distributions

“…In a recent series of papers, phase transition properties of infinite dimensional RFIM with symmetric double [55] and triple [56] Gaussian random fields have also been studied by means of a replica method and a rich variety of phase diagrams have been presented. The situation has also been handled on three dimensional lattices with nearest-neighbor interactions by a variety of theoretical works such as EFT [57,58], EFT with multi site spin correlations [59], MC simulations [60][61][62], pair approximation [63], and the series expansion method [64].…”

Effects of the randomly distributed magnetic field on the phase diagrams of the Ising Nanowire II: Continuous distributions

“…In a recent series of papers, phase transition properties of infinite dimensional RFIM with symmetric double [54] and triple [55] Gaussian random fields have also been studied by means of a replica method and a rich variety of phase diagrams have been presented. The situation has also been handled on 3D lattices with nearest-neighbor interactions by a variety of theoretical works such as EFT [56,57], EFT with multi site spin correlations [58], MC simulations [59][60][61], pair approximation [62], and the series expansion method [63].…”