LINEAR-POLYMERS WITH COMPETING INTERACTIONS - SWOLLEN LINEAR, SWOLLEN BRANCHED, AND COMPACT SCALING REGIMES

Models of linear polymers with competing interactions favoring ramification into thin branches on one hand, and compactification on the other hand, are shown to possess a phase diagram with swollen linear, swollen branched, and compact regimes. Between each pair of these regimes, a multicritical transition occurs. The three transitions merge in a single, very unstable multicritical point. Evidence of such behavior is obtained by renormalization methods applied exactly to a model on a hierarchical lattice, and approximately to a system on a square lattice. The hierarchical model calculations, discussed in much detail, are particularly extensive and give the advantage of an almost complete characterization of the different scaling behaviors, exact at least within the limits of numerical accuracy. The strong qualitative evidence from renormalization group approaches is further confirmed by an extensive exact enumeration analysis for a third model on the square lattice. The scalings at various multicritical transitions are studied in detail and universality issues are discussed.