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

Models of linear polymers with competing interactions favoring ramific ation into thin branches on one hand, and compactification on the othe r hand, are shown to possess a phase diagram with swollen linear, swol len branched, and compact regimes. Between each pair of these regimes, a multicritical transition occurs. The three transitions merge in a s ingle, very unstable multicritical point. Evidence of such behavior is obtained by renormalization methods applied exactly to a model on a h ierarchical lattice, and approximately to a system on a square lattice . The hierarchical model calculations, discussed in much detail, are p articularly extensive and give the advantage of an almost complete cha racterization of the different scaling behaviors, exact at least withi n the limits of numerical accuracy. The strong qualitative evidence fr om renormalization group approaches is further confirmed by an extensi ve exact enumeration analysis for a third model on the square lattice. The scalings at various multicritical transitions are studied in deta il and universality issues are discussed.