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

An Ising model with ferromagnetic nearest-neighbor interactions J1J1 (J1>0J1>0) and random next-nearest-neighbor interactions [+J2+J2 with probability p   and −J2−J2 with probability (1−p)(1−p); J2>0J2>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=1,2n=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=J2J1=J2, showing both superantiferromagnetic (low p) and ferromagnetic (higher values of p) orderings at low temperatures.