Anisotropy and marginality in the two-dimensional fully frustrated Ising model

The effect of anisotropy is investigated in the two-dimensional fully frustrated Ising model on a square lattice. It is shown that the anisotropy acts like a symmetry-breaking field by lowering the symmetries of the ground state. The stress tensor is found to be a relevant operator at $T=0\mathrm{}$. A particular form of anisotropy which does not destroy the critical behavior is also studied. The introduction of a special second-neighbor interaction leads to continuous change of the exponent $\eta$.