J. Phys. I France 6 (1996) 1305-1320
DOI: 10.1051/jp1:1996246

Random Surface Discretizations and the Renormalization of the Bending Rigidity

G. Gompper^{1, 2} and D.M. Kroll<sup>3

1</sup>  Max-Planck-Institut fur Kolloid- und Grenzflachenforschung, Kantstrasse 55, 14513 Teltow,Germany
²  Sektion Physik der Ludwig-Maximilians-Universitat Munchen, Theresienstrasse 37,80333 Munchen, Germany
³  Department of Medicinal Chemistry, and Minnesota Supercomputer Institute,University of Minnesota, 308 Harvard Street SE, Minneapolis, MN 55455, USA

(Received 15 March 1996, accepted 12 June 1996)

Abstract
The effect of thermal fluctuations on the properties of fluid vesicles is studied using Monte Carlo simulations and scaling arguments. It is shown that the commonly used discretization of the bending energy on triangulated surfaces - which is based on the squared difference of unit normal vectors of neighboring triangles - is problematic because the relation between the coupling constant \delta and the bending rigidity n is shape dependent (in the limit \delta \to infinity). In contrast, discretizations based on the square of local averages of the mean curvature do not share this problem. Nevertheless, the scaling behavior of spherical vesicles is found to be unaffected by this deficiency of the former discretization. An explicit calculation of the average volume (V) in the large-n limit reveals that (V) is not a homogeneous function of the persistence length \xi_P and the vesicle radius, but that there is a weak breakdown of scaling, with a logarithmic correction term of the form ln(4\pi\kappa/3). Monte Carlo data obtained using both discretizations are consistent with this prediction and provide clear evidence for a n-dependence of the persistence length of the form \xi_P \sim exp[4\pi\kappa/3], in agreement with field-theoretic renormalization group results.

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