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

TL;DR

This study investigates the crumpling transition of a discretized triangular lattice model, introducing a modified folding rule compatible with periodic boundaries, and analyzes multiple phase transitions with estimated latent heats.

Contribution

It proposes a modified folding constraint that allows for periodic boundary conditions, enabling more efficient transfer-matrix analysis of crumpling transitions.

Findings

Identified multiple crumpling transition points at specific bending rigidity values.

Estimated latent heats associated with each transition.

Reduced transfer-matrix size through the 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.