Differential renormalization of van der Waals spin models

An exact renormalization group equation in differential form is derived for spin systems with general many-body interactions in the van der Waals limit. This equation is solved and the free energy is determined as an integral along the renormalization trajectory in the interaction space. It is shown that the transformation can always be modified in such a way that an undetermined integration constant for the free energy vanishes exactly, also below the critical temperature. We also demonstrate how the invariance of the free energy under a parameterdependent equivalence transformation can provide information about the critical behavior of the system. In this alternative approach "dangerous" irrelevant variables play an essential role