  In this paper we consider a 2d random Ising system on a square lattice with
nearest neighbour interactions. The disorder is short range correlated and
asymmetry between the vertical and the horizontal direction is admitted. More
precisely, the vertical bonds are supposed to be non random while the
horizontal bonds alternate: one row of all non random horizontal bonds is
followed by one row where they are independent dichotomic random variables. We
solve the model using an approximate approach that replace the quenched average
with an annealed average under the constraint that the number of frustrated
plaquettes is keep fixed and equals that of the true system. The surprising
fact is that for some choices of the parameters of the model there are three
second order phase transitions separating four different phases:
antiferromagnetic, glassy-like, ferromagnetic and paramagnetic.
