New singularities in the critical behavior of random Ising models at marginal dimensionalities

Renormalization-group equations are exactly solved for the random Ising model with (i) short-range interaction at $d=4$, and (ii) dipolar interactions at $d=3$. In both cases, the leading singularities of the susceptibility χ and of the specific heat C are found to be χ∝t^-1exp[(D|lnt|)1/2] and C∝-|lnt|1/2exp[-2(D|lnt|)1/2] as t=(T-Tc)Tc→0. D is a universal constant, equal to 6/53 in case (i) and to 9/[81ln(4/3) + 53] in case (ii). Relations between amplitudes of C and of the correlation length, corrections to the leading singularities, crossover effects from the nonrandom region or from the meanfield region to the asymptotic critical region and possible experiments are also discussed.