Renormalization group analysis of the finite two-dimensional XY model with fourfold anisotropy: Application to the magnetic susceptibility of a ferromagnetic ultrathin film

The renormalization group equations describing a finite 2DXY (two-dimensional XY) system with fourfold anisotropy are solved in two steps, in order to study the magnetic transition to paramagnetism in an ultrathin film. First, the equations are linearized near the critical coupling K=J/kBT=2/π. This allows integration constants to be evaluated at the fixed point, and the tuning of the constants to represent a ferromagnetic ultrathin film. An …