  We derive the effective potential for composite fields in a class of (quasi-)
planar models with long-range interactions. This class of models can be
relevant for high temperature superconductors and graphite. The fractal
structure of the effective potential is revealed and its physical
interpretation is presented. It is argued that the multi-branched fractal
structure of the potential reflects the presence of an infinite tower of
excitonic bound states that occur as a result of the long-range interactions.
