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

Abstract

Folding of the triangular lattice in a discrete three-dimensional space is investigated numerically. Such ``discrete folding'' has come under through theoretical investigation, since Bowick and co-worker 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 L \le 6. 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.

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Cited by in corpus (11)

• Monte Carlo studies of a Finsler geometric surface model
• Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule
• Monte Carlo studies of triangulated spherical surfaces in the two-dimensional space
• Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime
• Branched-polymer to inflated transition of self-avoiding fluid surfaces
• Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling
• Phase structure of a surface model with many fine holes
• First-order phase transition of triangulated surfaces on a spherical core
• Shape transformations of a model of self-avoiding triangulated surfaces of sphere topology
• Crumpled-to-tubule transition and shape transformations of a model of self-avoiding spherical meshwork
• In-plane deformation of a triangulated surface model with metric degrees of freedom