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

Abstract

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 of the transfer-matrix size. Treating the cluster sizes L \le 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.

References in corpus (5)

• Crumpling transition and flat phase of polymerized phantom membranes
• First-order transition of tethered membranes in 3d space
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• Folding of the triangular lattice in a discrete three-dimensional space: Density-matrix-renormalization-group study
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Cited by in corpus (2)

• Crumpling transition of the discrete planar folding in the negative-bending-rigidity regime
• In-plane deformation of a triangulated surface model with metric degrees of freedom