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 (J(x,y)) and isotropic next-nearest neighbor (J(d)) 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 J(d) = -1/2 | J(x,y| min )if J(x) and J(y )have the same sign or J(d )=1/2 |J(x,y)|(min )if J(x )and J(y) have opposite signs( )