Multicritical points in an Ising random-field model

Abstract

The phase diagram of the mean-field Ising model in a random field obeying a symmetric threepeak distribution is determined. This distribution is relevant to diluted antiferromagnets in a uniform magnetic field. The phase diagram includes a fourth-order point, tricritical points, ordered critical points, critical end points, and a double critical end point. An ordered phase persists for arbitrarily large random fields at low temperatures.

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

“…The criteria for determining the order of the low temperature phase transition and its dependence on the form of the field distribution have been discussed throughout the years [37,[67][68][69][70][71][72][73]. In fact, different results have been proposed for different field distributions, like the existence of a tricritical point at the strong disorder regime of the system, present only in the bimodal distribution [37,69].…”

Tricritical points in the Sherrington-Kirkpatrick model in the presence of discrete random fields

“…We have studied the Sherrington-Kirkpatrick spin glass in the presence of random fields {h i }, following a trimodal (three-peak) probability distribution, which corresponds to a bimodal plus a probability p 0 for field dilution, i.e., P ( distribution [15] is washed way by the presence of the delta at the origin, whenever p 0 becomes greater than a certain value [17,18].…”

“…Indeed, Aharony [15] argued that whenever an analytic symmetric distribution for the fields presents a minimum at zero field, one should expect a tricritical point and a first-order transition for sufficiently low temperatures. Further studies of the RFIM at the mean-field level have considered a trimodal (three-peak) distribution [17,18] (1 − p 0 ). Such a distribution, which may be interpreted as a bimodal added to a dilution in the fields with probability p 0 [17], is expected to mimic better real systems than its bimodal counterpart.…”

Universality in four-dimensional random-field magnets

“…This in turn indicated that the two models should be in the same universality class. Further studies along these lines, using meanfield and renormalization-group approaches, provided contradicting evidence for the critical aspects of the p = 1/3 model and also proposed several approximations of its phase diagram for a range of values of p [40][41][42]. Only very recently accurate numerical data at zero temperature have been presented at d = 3, indicating that the original suggestion of Mattis is most probably correct [43].…”