Mean-field glassy phase of the random-field Ising model

The emergence of glassy behavior of the random-field Ising model (RFIM) is investigated using an extended mean-field theory approach. Using this formulation, systematic corrections to the standard Bragg-Williams theory can be incorporated, leading to the appearance of a glassy phase, in agreement with the results of the self-consistent screening theory of Mezard and Young. Our approach makes it also possible to obtain information about the low-temperature behavior of this glassy phase. We present results showing that within our mean-field framework, the hysteresis and avalanche behavior of the RFIM is characterized by power-law distributions, in close analogy with recent results obtained for mean-field spin-glass models.