Dynamic susceptibility for Ising-spin clusters in random fields

The dynamic susceptibility for a cluster of six coupled random field Ising spins in two different distributions, binary (ED) and Gaussian (GD), are calculated and exact results are obtained. The real and imaginary parts of the dynamic susceptibility display maxima when plotted versus temperature. These maxima can be described by an Arrhenius law. If the logarithm of the susceptibilities is plotted as a function of the logarithm of frequency and if the clusters are frustrated, then the real part displays a sequence of plateau regions and the imaginary part has a sequence of maxima in weak random fields. In the ED case of random field for large amplitudes there is only one plateau and one corresponding maximum as in ferromagnetic (FM) and paramagnetic (PM) cases. Our results confirm that any weak random field spill turn out to destroy the ordered state and random field Ising-spin clusters behave like Ising-spin glasses.