Interacting crumpled manifolds: Exact results to all orders of
perturbation theory
Henryk A. Pinnow1, Kay Jörg Wiese1,2
1Fachbereich Physik, Uni Essen, 45117 Essen, Germany
2KITP, University of California at Santa Barbara, CA 93106,
USA
Abstract
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 g of the interaction exactly in the limit of internal
dimension D -> 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)4, where again all orders in g 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.
cond-mat/0210007 [pdf]
Europhys. Lett. 64 (2003) 371-377 [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.