Crumpling transition of the discrete planar folding in the negative-bending-rigidity regime

The folding of the triangular lattice embedded in two dimensions (discrete planar folding) is investigated numerically. As the bending rigidity K varies, the planar folding exhibits a series of crumpling transitions at K≈-0.3 and K≈0.1. By means of the transfer-matrix method for the system sizes L≤14, we analyze the singularity of the transition at K≈-0.3. As a result, we estimate the transition point and the latent heat as K=-0.270 (2) and Q=0.043 (10), respectively. This result suggests that the singularity belongs to a weak-first-order transition.