Stiffening of fluid membranes due to thermal undulations: density matrix   renormalization group study
  It has been considered that the effective bending rigidity of fluid membranes should be reduced by thermal undulations. However, recent thorough investigation by Pinnow and Helfrich revealed significance of measure factors for the partition sum. Accepting the local curvature as a statistical measure, they found that fluid membranes are stiffened macroscopically. In order to examine this remarkable idea, we performed extensive ab initio simulations for a fluid membrane. We set up transfer matrix which is diagonalized by means of the density-matrix renormalization group. Our method has an advantage in that it allows us to survey various statistical measures. As a consequence, we found that the effective bending rigidity flows toward strong coupling under the choice of local curvature as a statistical measure. On the contrary, for other measures such as normal displacement and tilt angle, we found clear tendency toward softening. 
Yoshihiro Nishiyama (Okayama University)