2010/03/10 by Yoshihiro Nishiyama
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Block Copolymer Self-Assembly #Boundary value problem #Computer science #Condensed matter physics #Discretization #Flexural rigidity #Gravitational singularity #Hexagonal lattice #Lattice (music) #Mathematical analysis #Mathematics #Periodic boundary conditions #Physics #Theoretical and Computational Physics #Thermodynamics #Transfer matrix #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.81.041116
published as Phys. Rev. E 81, 041116 (2010).
arxiv created 2010/03/10 · openalex publication_date 2010/04/16 · arxiv updated 2015/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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<or=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.