Two-dimensional polymeric liquids and polymer stars: learning from conflicting theories
Résumé
We discuss systems for which two carefully derived, yet conflicting, theories coexisted. Dense polymers in two dimensions and star-shaped polymers in the θ-regime are considered. In both cases the two proposed theories are in a sense exact, but turn out to satisfy different crossing rules (for the 2d polymer) or to correspond to different orders of limits. Finally, both theories prove very useful, albeit for different subclasses of physical systems.