Spontaneous magnetization of the square 2D Ising lattice with nearest- and weak next-nearest-neighbour interactions

We show that the square two-dimensional (2D) Ising lattice with nearest- (J) and weak next-nearest-neighbour interactions (Jd) can be mapped on a square 2D Ising lattice that has only nearest neighbour interactions (J*). For Jd/J << 1 the transformation equation has the simple form  [image omitted]. This result can be used to derive expressions for several thermodynamic functions of the square 2D Ising lattice with weak next-nearest-neighbour interactions. As an example we consider the spontaneous magnetization and compare it with low-temperature series expansion results.