Interacting crumpled manifolds
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 paper we study the effect of a δ-interaction on a polymerized membrane
of arbitrary internal dimension D. Depending on the dimensionality of the
membrane and embedding space, different physical scenarios are observed. We
emphasize the difference of polymers from membranes. For the latter, nontrivial
contributions appear at the two-loop level. We also exploit a `massive scheme'
inspired by calculations in fixed dimensions for scalar field theories. Despite
the fact that these calculations are only amenable numerically, we found that in
the limit of D → 2 each diagram can be evaluated analytically. This property
extends in fact to any order in perturbation theory, allowing for a summation
of all orders. This is a novel and quite surprising result. Finally, an attempt
to go beyond D = 2 is presented. Applications to the case of selfavoiding
membranes are mentioned.
cond-mat/0210007 [pdf]
J. Phys. A 35 (2002) 1195-1229 [pdf]
Copyright (C) by Kay Wiese. Last edited November 14, 2011.