J. Phys. II France
Volume 4, Numéro 6, June 1994
Page(s) 931 - 949
DOI: 10.1051/jp2:1994175
J. Phys. II France 4 (1994) 931-949

Measure factors, tension, and correlations of fluid membranes

W. Cai, T.C. Lubensky, P. Nelson and T. Powers

Physics Department, University of Pennsylvania, Philadelphia, PA 19104 U.S.A.

(Received 18 January 1994, accepted 10 March 1994)

We study two geometrical factors needed for the correct construction of statistical ensembles of surfaces. Such ensembles appear in the study of fluid bilayer membranes, though our results are more generally applicable. The naive functional measure over height fluctuations must be corrected by these factors in order to give correct, self-consistent formulas for the free energy and correlation functions of the height. While one of these corrections - the Faddeev-Popov determinant - has been studied extensively, our derivation proceeds from very simple geometrical ideas, which we hope removes some of its mystery. The other factor is similar to the Liouville correction in string theory. Since our formulas differ from those of previous authors, we include some explicit calculations of the effective frame tension and two-point function to show that our version indeed secures coordinate-invariance and consistency to lowest nontrivial order in a temperature expansion.

© Les Editions de Physique 1994