Folding of the triangular lattice in a discrete three-dimensional space: Density-matrix renormalization-group study

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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 [Formula presented]. Aiming to surmount this limitation, we utilized the density-matrix renormalization group. Thereby, we succeeded in treating strip widths up to [Formula presented] 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.

Original languageEnglish
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume70
Issue number1
DOIs
Publication statusPublished - Jan 1 2004

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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