Phase diagram of the two-dimensional Ising model with random competing interactions

An Ising model with ferromagnetic nearest-neighbor interactions J₁ (J₁>0) and random next-nearest-neighbor interactions [+J₂ with probability p and −J₂ with probability (1−p); J₂>0] is studied within the framework of an effective-field theory based on the differential-operator technique. The order parameters are calculated, considering finite clusters with n=1,2, and 4 spins, using the standard approximation of neglecting correlations. A phase diagram is obtained in the plane temperature versus p, for the particular case J₁=J₂, showing both superantiferromagnetic (low p) and ferromagnetic (higher values of p) orderings at low temperatures.