Griffith singularities in the random-field Ising model

Abstract

The D-dimensional ferromagnetic Ising model with weak Gaussian random fields is considered. In dimensions D<3 due to rare large-scale thermal excitations (large-spin clusters with magnetization opposite to the ferromagnetic background) in the low-temperature region h02<<T<<1 (where h0 is the characteristic value of the field) the free energy is shown to contain a non-analytic contribution of the form exp(-(const/2h02)(h02/T)(3-D/2)).