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Linear polymers with competing interactions: Swollen linear, swollen branched, and compact scaling regimes

R. Dekeyser

E. Orlandini

A. L. Stella

M. C. Tesi

  • Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, B-3001 Heverlee, Belgium

  • Department of Physics, Theoretical Physics, University of Oxford, Oxford OX1 3NP, England

  • Istituto Nazionale di Fisica della Materia, Dipartimento di Fisica e Sezione Istituto Nazionale di Fisica Nucleare, Università di Padova, I-35131 Padova, Italy

  • Mathematical Insitute, University of Oxford, Oxford OX1 3NP, England

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Phys. Rev. E 52, 5214 – Published 1 November, 1995

DOI: https://doi.org/10.1103/PhysRevE.52.5214

Abstract

Models of linear polymers with competing interactions favoring ramifications 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.

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Phys. Rev. E 52, 5214– Published 1 November, 1995
  • Received 6 April 1995

© 1995 American Physical Society

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