Europhys. Lett.
Volume 64, Number 3, November 2003
Page(s) 371 - 377
Section Condensed matter: structure, mechanical and thermal properties
Published online 01 November 2003
DOI: 10.1209/epl/i2003-00204-2
Europhys. Lett., 64 (3) , pp. 371-377 (2003)

Interacting crumpled manifolds: Exact results to all orders of perturbation theory

H. A. Pinnow1 and K. J. Wiese2

1  Fachbereich Physik, Universität Essen - 45117 Essen, Germany
2  KITP, Kohn Hall, University of California at Santa Barbara Santa Barbara, CA 93106, USA

(Received 1 October 2002; accepted in final form 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 $D\rightarrow 2$. This exact solution is the starting point for an expansion in 2-D, which aims at connecting to the well-studied case of polymers ( D=1). We here give results to order (2-D)2, 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.

68.35.Md - Surface thermodynamics, surface energies.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
11.10.-z - Field theory.

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