On Kadanoff's approximate renormalization group transformation

The fixed point structure resulting from the approximate renormalization group equations obtained by shifting bonds on the square Ising lattice is considered as a function of a free parameter h appearing in the definition of these equations. Next to the fixed point S considered by Kadanoff which is located in a symmetry plane two other “critical” fixed points A and B are found for h0.726. At the value h = 0.741, A crosses the fixed point S and vanishes together with the fixed point B at h = 0.726. Furthermore correction terms to the eigenvalues of the linearized renormalization group equations as obtained by Kadanoff are considered which arise if one chooses h to be optimal at all points of the coupling parameter space.