Renormalization group study of the two-dimensional Ising model with crossing bonds

The simple quadratic Ising model with nearest- and next-nearest-neighbor interactions is investigated by means of the mean field renormalization group approach. By conveniently choosing the size of the blocks one obtains the expected phase diagram exhibiting ferromagnetic, antiferromagnetic, paramagnetic and superantiferromagnetic phases. The critical lines which separate the paramagnetic phase from the ordered ones have the expected asymptotic behavior for large values of the nearest-neighbor coupling.