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 ther mal excitations (large-spin clusters with magnetization opposite to th e ferromagnetic background) in the low-temperature region h0(2) much l ess than T much less than 1 (where h0 is the characteristic value of t he field) the free energy is shown to contain a non-analytic contribut ion of the form exp[-(const/2h0(2))(h0(2)/T)(3-D)/2].