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

Abstract

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.