Volume 64, Number 3, November 2003
|Page(s)||371 - 377|
|Section||Condensed matter: structure, mechanical and thermal properties|
|Published online||01 November 2003|
Interacting crumpled manifolds: Exact results to all orders of perturbation theory
Fachbereich Physik, Universität Essen - 45117 Essen, Germany
2 KITP, Kohn Hall, University of California at Santa Barbara Santa Barbara, CA 93106, USA
Accepted: 20 August 2003
In this letter, we report progress on the field theory of polymerized tethered membranes. For the toy model of a manifold repelled by a single point, we are able to sum the perturbation expansion in the strength g0 of the interaction exactly in the limit of internal dimension . This exact solution is the starting point for an expansion in , which aims at connecting to the well-studied case of polymers (). We here give results to order , where again all orders in g0 are resummed. This is a first step towards a more complete solution of the self-avoiding manifold problem, which might also prove valuable for polymers.
PACS: 68.35.Md – Surface thermodynamics, surface energies / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 11.10.-z – Field theory
© EDP Sciences, 2003
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