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ID 30181
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Author
Nishiyama, Yoshihiro Kaken ID publons researchmap
Abstract

Folding of the triangular lattice in a discrete three-dimensional space is investigated numerically. Such "discrete folding" has come about through theoretical investigation, since Bowick and co-workers introduced it as a simplified model for the crumpling of the phantom polymerized membranes. So far, it has been analyzed with the hexagon approximation of the cluster variation method (CVM). However, the possible systematic error of the approximation was not fully estimated; in fact, it has been known that the transfer-matrix calculation is limited in the tractable strip widths Lless than or equal to6. Aiming to surmount this limitation, we utilized the density-matrix renormalization group. Thereby, we succeeded in treating strip widths up to L=29 which admit reliable extrapolations to the thermodynamic limit. Our data indicate an onset of a discontinuous crumpling transition with the latent heat substantially larger than the CVM estimate. It is even larger than the latent heat of the planar (two-dimensional) folding, as first noticed by the preceding CVM study. That is, contrary to our naive expectation, the discontinuous character of the transition is even promoted by the enlargement of the embedding-space dimensions. We also calculated the folding entropy, which appears to lie within the best analytical bound obtained previously via combinatorics arguments.

Keywords
crystalline random surfaces
crumpling transition
statisticalmechanics
tethered surfaces
membranes
phase
Note
Digital Object Identifer:10.1103/PhysRevE.70.016101
Published with permission from the copyright holder. This is the institute's copy, as published in Physical Review E, July 2004, Volume 70, Issue 1, Pages 7.
Publisher URL:http://dx.doi.org/10.1103/PhysRevE.70.016101
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Copyright © 2004 The American Physical Society. All rights reserved.
Published Date
2004-7
Publication Title
Physical Review E
Volume
volume70
Issue
issue1
Content Type
Journal Article
language
英語
Refereed
True
DOI
Web of Science KeyUT
Submission Path
electricity_and_magnetism/176