Crumpling transition of the triangular lattice without open edges: Effect of a modified folding rule

Folding of the triangular lattice in a discrete three-dimensional space is investigated by means of the transfer-matrix method. This model was introduced by Bowick and co-workers as a discretized version of the polymerized membrane in thermal equilibrium. The folding rule (constraint) is incompatible with the periodic-boundary condition, and the simulation has been made under the open-boundary condition. In this paper, we propose a modified constraint, which is compatible with the periodic-boundary condition; technically, the restoration of translational invariance leads to a substantial reduction in the transfer-matrix size. Treating the cluster sizes L≤7, we analyze the singularities of the crumpling transitions for a wide range of the bending rigidity K. We observe a series of the crumpling transitions at K=0.206 (2), -0.32 (1), and -0.76 (10). At each transition point, we estimate the latent heat as Q=0.356 (30), 0.08(3), and 0.05(5), respectively.