Novel Phase Diagram for Self-Avoiding Walks (Polymers)

The analogy between self-avoiding walks and the zero-component magnetic system on a lattice is considered. The magnetic system possesses a natural boundary in the ($T-H$) plane below which we cannot continue it analytically. It is found, however, that we do not have to cross this boundary to obtain the semidilute regime. The scaling relation of des Cloizeaux is confirmed. There is also discovered a new phase below the boundary which is identified as a collapsed phase. This is quite unexpected because no attractive interactions are allowed.