  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
-infty < K < infty. In this paper, we investigate the K<0 regime, for which the
CVM analysis with the single-hexagon-cluster approximation predicts two types
of (crumpling) transitions of both continuous and discontinuous characters. We
diagonalized the transfer matrix for the strip widths up to L=26 with the aid
of the density-matrix renormalization group. Thereby, we found that
discontinuous transitions occur successively at K=-0.76(1) and -0.32(1).
Actually, these transitions are accompanied with distinct hysteresis effects.
On the contrary, the latent-heat releases are suppressed considerably as
Q=0.03(2) and 0.04(2) for respective transitions. These results indicate that
the singularity of crumpling transition can turn into a weak-first-order type
by appreciating the fluctuations beyond a meanfield level.
