The Random Field Problem; Facts and Fiction

Abstract

Site random fields have profound effects on the ground state properties and critical behavior of magnetically ordered systems. For the random field Ising model (RFIM), it has been proven theoretically that the lower critcal dimension dl = 2. A variety of experimental studies by the author and his colleagues on RFIM systems have demonstrated the phase transition to be destroyed at d = 2 and a sharp, continuous phase transition at TC(H) to exist at d = 3 with new critical exponents corresponding to an effective dimensionality \( \bar{d} \simeq 2 \); suggestive of a dimensionality reduction \( \bar{d} \simeq d - 1 \). Furthermore, extreme critical slowing down has been observed as T→TC(H). This explains why field cooling through TC(H) always traps the d=3 system into a nonequilibrium domain state on what are laboratory time scales. The predicted crossover scaling has been observed for the field dependence of all thermodynamic functions and “phase boundaries” in the dis-tinctly different d=2 and d=3 RFIM systems. Contrary to current theory and the results described above, Birgeneau, Cowley and Shirane — from neutron scattering studies alone — have 1) assumed the low-temperature, field-cooled configuration is always the ground state of the RFIM, 2) “unambiguously” determined dl ≥ 3 and 3) discovered a “temporal” and/or discontinuous phase transition occurs at d=3. I suggest the errors in all of their conclusions represent a confluence of the limitations of the use of a single experimental technique, not doing the key experiments with that technique, incorrect interpretations and a concomitant use of poor and/or badly characterized materials.