Random surface discretizations and the renormalization of the bending rigidity

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 lambda and the bending rigidity kappa is shape dependent (in the limit lambda --> 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-rc 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 kappa-dependence of the persistence length of the form xi(p) similar to exp[4 pi kappa/3], in agreement with field-theoretic renormalization group results.