  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.
