Beta Function Constraints from Renormalization Groups Flows in Spin Systems

Inspired by previous work on the constraints that duality imposes on beta functions of spin models, we propose a consistency condition between those functions and RG flows at different points in coupling constant space. We show that this consistency holds for a non self-dual model which admits an exact RG flow, but that it is violated when the RG flow is only approximate. We discuss the use of this deviation as a test for the ``goodness'' of proposed RG flows in complicated models, and the use of the proposed consistency in suggesting RG equations.