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

TL;DR

This study numerically investigates the crumpling transitions in discrete planar folding of a triangular lattice, identifying a weak-first-order transition at negative bending rigidity with specific transition point and latent heat.

Contribution

It provides the first numerical analysis of crumpling transitions in discrete planar folding in the negative-bending-rigidity regime, estimating transition parameters and characterizing the transition type.

Findings

Transition point at K=-0.270(2)

Latent heat estimated as Q=0.043(10)

Transition identified as weak-first-order

Abstract

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 \approx -0.3 and K \approx 0.1. By means of the transfer-matrix method for the system sizes L \le 14, we analyze the singularity of the transition at K \approx -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.