Morphological transitions of the fixed-point potential of the renormalization group

Interactions between fluid membranes are studied by renormalization group techniques. To make the zero-flow condition at the origin compatible with the renormalization, there should be a nonrenormalizable region near the origin. The renormalization procedure involving such a region picks up an inhomogeneous contribution which will also be recast during the renormalization. This paper gives an example to show how the morphology of the fixed-point potential undergoes a series of transitions due to this inhomogeneous contribution.