GRIFFITH SINGULARITIES IN THE RANDOM-FIELD ISING-MODEL

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 h0(2) much less than T much less than 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/2h0(2))(h0(2)/T)(3-D)/2].