Phase diagram of the square 2D Ising lattice with nearest neighbor and next-nearest neighbor interactions

We have determined the temperature dependent phase diagram of the square 2D Ising lattice with anisotropic nearest neighbor ((Formula presented.)) and isotropic next-nearest neighbor ((Formula presented.)) interactions. The phase boundaries between the various ordered phases (ferromagnetic, antiferromagnetic and striped antiferromagnetic) and the disordered phase (paramagnetic) are obtained by considering the domain wall free energy. Although the phase boundary equations are not exact, they provide a very accurate description when the nearest neighbor interactions are stronger than the next-nearest neighbor interaction. The square 2D Ising lattice does not exhibit a phase transition when (Formula presented.) if (Formula presented.) and (Formula presented.) have the same sign or (Formula presented.) if (Formula presented.) and (Formula presented.) have opposite signs.