Scaling behavior of tethered crumpled manifolds with inner dimension
close to D=2: Resumming the perturbation theory
Henryk A. Pinnow1, Kay Jörg Wiese1,2
1Fachbereich Physik, Uni Essen, 45117 Essen,
Germany
2Laboratoire de Physique Théorique,
Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
Abstract
The field theory of self-avoiding tethered
membranes still poses major challenges. In this article, we report
progress on the toy-model of a manifold repelled by a single
point. Our approach allows to sum the perturbation expansion in the
strength g0 of the interaction exactly in the limit
of internal dimension D -> 2, yielding an analytic solution for
the strong-coupling limit. This analytic 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 give results to fourth order
in 2-D, where the dependence on g0 is again
summed exactly. As an application, we discuss plaquette density
functions, and propose a Monte-Carlo experiment to test our
results. These methods should also allow to shed light on the more
complex problem of self-avoiding manifolds.
cond-mat/0403734 [pdf]
Nucl. Phys. B 711 (2005) 530-564 [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.