Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-09-30
Physics
Condensed Matter
Statistical Mechanics
LaTeX+revtex4+eps figures. 129 pages. A few changes in the introduction section
Scientific paper
10.1007/s10955-005-5253-9
We compute the normalisation factor for the large order asymptotics of perturbation theory for the self-avoiding manifold (SAM) model describing flexible tethered (D-dimensional) membranes in d-dimensional space, and the epsilon-expansion for this problem. For that purpose, we develop the methods inspired from instanton calculus, that we introduced in a previous publication (Nucl. Phys. B 534 (1998) 555), and we compute the functional determinant of the fluctuations around the instanton configuration. This determinant has UV divergences and we show that the renormalized action used to make perturbation theory finite also renders the contribution of the instanton UV-finite. To compute this determinant, we develop a systematic large-d expansion. For the renormalized theory, we point out problems in the interplay between the limits epsilon->0 and d->infinity, as well as IR divergences when epsilon= 0. We show that many cancellations between IR divergences occur, and argue that the remaining IR-singular term is associated to amenable non-analytic contributions in the large-d limit when epsilon= 0. The consistency with the standard instanton-calculus results for the self-avoiding walk is checked for D = 1.
David Francois
Wiese Kay J.
No associations
LandOfFree
Instanton calculus for the self-avoiding manifold model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Instanton calculus for the self-avoiding manifold model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Instanton calculus for the self-avoiding manifold model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-592857