Journal of Statistical Physics

, Volume 67, Issue 5–6, pp 1083–1108 | Cite as

Marriage of exact enumeration and 1/d expansion methods: Lattice model of dilute polymers

  • A. M. Nemirovsky
  • Karl F. Freed
  • Takao Ishinabe
  • Jack F. Douglas


We consider the properties of a self-avoiding polymer chain with nearestneighbor contact energyɛ on ad-dimensional hypercubic lattice. General theoretical arguments enable us to prescribe the exact analytic form of then-segment chain partition functionC n ,and unknown coefficients for chains of up to 11 segments are determined using exact enumeration data ind=2–6. This exact form provides the main ingredient to produce a large-n expansion ind−1of the chain free energy through fifth order with the full dependence on the contact energy retained. The ɛ-dependent chain connectivity constant and free energy amplitude are evaluated within thed−1expansion toO(d−5). Our general formulation includes for the first time self-avoiding walks, neighboravoiding walks, theta, and collapsed chains as particular limiting cases.

Key words

Lattice model of polymers self-avoiding walk self-interacting walk neighbor-avoiding walk connectivity constant 


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Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • A. M. Nemirovsky
    • 1
  • Karl F. Freed
    • 1
  • Takao Ishinabe
    • 2
  • Jack F. Douglas
    • 3
  1. 1.James Franck InstituteUniversity of ChicagoChicago
  2. 2.Faculty of EngineeringYamagata UniversityYonezawaJapan
  3. 3.Polymers DivisionNational Institute of Standards and TechnologyGaithersburg

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