The random-field Ising model at high magnetic concentration

Abstract

During the project period we have largely completed our characterization of the critical behavior of the random-field Ising model (RFIM) transition in three dimensions (d = 3). This has been a long sought-after goal, the transition having been first observed in the early 1980's [1, 2]. Our thinking about the phase transition in the RFIM was greatly advanced when we discovered a few years ago that one has to work at concentrations x > x v = 0.76, the magnetic vacancy percolation threshold concentration [3, 4]. As described below, at lower concentrations, the transition is obscured by metastable domains. Once we realized this, we were able devote considerable effort to understanding the RFIM critical behavior to test theories and predictions from computer simulations. We applied neutron scattering, x-ray scattering, optical, specific heat, and other techniques to achieve a nearly complete characterization of this important phase transition, devoting most of our effort to one particular high magnetic concentration crystal Fe 0.85 Zn 0.15 F 2 . The Fe x Zn 1−x F 2 system has been well documented and studied as an ideal realization of the RFIM when subjected to an applied field along its easy axis. The significance of this particular phase transition is that it represents one of the major classes of randomness in ordering processes, distinct from random-exchange and spin-glass ordering. This baffling problem of ordering in the presence of random fields has now been brought by our experiments to a much higher level of understanding.