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Nonlocal effective-average-action approach to crystalline phantom membranes.
Phys Rev E Stat Nonlin Soft Matter Phys
March 2011
Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany.
We investigate the properties of crystalline phantom membranes, at the crumpling transition and in the flat phase, using a nonperturbative renormalization group approach. We avoid a derivative expansion of the effective average action and instead analyze the full momentum dependence of the elastic coupling functions. This leads to a more accurate determination of the critical exponents and further yields the full momentum dependence of the correlation functions of the in-plane and out-of-plane fluctuation.
View Article and Find Full Text PDFCrumpled-to-tubule transition in anisotropic polymerized membranes: beyond the ϵ expansion.
Phys Rev Lett
March 2011
LPTMC, CNRS UMR 7600, UPMC, 4 Place Jussieu, 75252 Paris Cedex 05, France.
Anisotropic D-dimensional polymerized phantom membranes are investigated within a nonperturbative renormalization group framework. One focuses on the transition between a high-temperature, crumpled phase and a low-temperature, tubular phase where the membrane is flat along one direction and crumpled along the other ones. While the upper critical dimension--D(uc)=5/2--is close to D=2, the weak-coupling perturbative approach is qualitatively and quantitatively wrong.
View Article and Find Full Text PDFCrumpling transition and flat phase of polymerized phantom membranes.
Phys Rev E Stat Nonlin Soft Matter Phys
April 2009
LPTM, CNRS UMR 8089, Université de Cergy-Pontoise, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France.
Polymerized phantom membranes are revisited using a nonperturbative renormalization-group approach. This allows one to investigate both the crumpling transition and the low-temperature flat phase in any internal dimension D and embedding dimension d and to determine the lower critical dimension. The crumpling phase transition for physical membranes is found to be of second order within our approximation.
View Article and Find Full Text PDFAnomalous elasticity in nematic and smectic elastomer tubule phases.
Phys Rev E Stat Nonlin Soft Matter Phys
September 2008
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
We study anomalous elasticity in the tubule phases of nematic and smectic elastomer membranes, which are flat in one direction and crumpled in another. These phases share the same macroscopic symmetry properties including spontaneously broken in-plane isotropy and hence belong to the same universality class. Below an upper critical value D_{c}=3 of the membranes' intrinsic dimension D , thermal fluctuations renormalize the elasticity with respect to elastic displacements along the tubule axis so that elastic moduli for compression along the tubule axis and for bending the tubule axis become length-scale dependent.
View Article and Find Full Text PDFFolding of the triangular lattice in a discrete three-dimensional space: crumpling transitions in the negative-bending-rigidity regime.
Phys Rev E Stat Nonlin Soft Matter Phys
September 2005
Department of Physics, Faculty of Science, Okayama University, Okayama 700-8530, Japan.
Folding of the triangular lattice in a discrete three-dimensional space is studied numerically. Such "discrete folding" was introduced by Bowick and co-workers as a simplified version of the polymerized membrane in thermal equilibrium. According to their cluster-variation method (CVM) analysis, there appear various types of phases as the bending rigidity K changes in the range -infinity
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