where S i z is the Ising dipole moments. The J i j refers to the random bond interactions which are described by a gaussian probability distribution with mean J 0 and variance J 2 / N . The second term provides a description of the interactions of the pseudo-spins in presence of random local fields where f i are represented by an independent gaussian distribution with zero mean and variance Δ Δ . The final term denotes the interaction in presence of an external electric field E .