Tethered membranes with long-range interactions

Emmanuel Guitter and John Palmeri
Phys. Rev. A 45, 734 – Published 1 January 1992
PDFExport Citation

Abstract

We treat the problem of D-dimensional tethered (or polymerized) membranes with long-range repulsive interactions (varying as 1/rγ) in a d-dimensional embedding space using both large-d and variational methods. We find three different regimes in the (γ,D) plane: for small D, the manifold is always crumpled, either Gaussian or swollen (with the exact exponent for the radius of gyration ν=2D/γ); for intermediate D, it undergoes a crumpling transition; and for large D, it is always flat. By extrapolating these results to the case of short-range interactions, we propose a phase diagram in the (d,D) plane for the still poorly understood problem of self-avoiding manifolds. The physical point D=2 and d=3 lies at the boundary of the always-flat region. This may provide an explanation for the recent numerical simulations that seemingly show that self-avoidance always makes two-dimensional membranes flat.

  • Received 22 July 1991

DOI:https://doi.org/10.1103/PhysRevA.45.734

©1992 American Physical Society

Authors & Affiliations

Emmanuel Guitter and John Palmeri

  • Service de Physique Théorique, Centre d’Etudes de Saclay, F-91191 Gif-sur-Yvette CEDEX, France

References (Subscription Required)

Click to Expand
Issue

Vol. 45, Iss. 2 — January 1992

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×