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Polymers 2018, 10(12), 1360; https://doi.org/10.3390/polym10121360

Parallel Tempering Monte Carlo Studies of Phase Transition of Free Boundary Planar Surfaces

1
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskiye Gory, MSU, 2-nd Educational Building, Moscow 119991, Russia
2
Department of Industrial Engineering, National Institute of Technology, Ibaraki College, Nakane 866, Hitachinaka, Ibaraki 312-8508, Japan
*
Author to whom correspondence should be addressed.
Received: 26 October 2018 / Revised: 2 December 2018 / Accepted: 5 December 2018 / Published: 8 December 2018
(This article belongs to the Special Issue Simulations of Polymers)
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Abstract

We numerically study surface models defined on hexagonal disks with a free boundary. 2D surface models for planar surfaces have recently attracted interest due to the engineering applications of functional materials such as graphene and its composite with polymers. These 2D composite meta-materials are strongly influenced by external stimuli such as thermal fluctuations if they are sufficiently thin. For this reason, it is very interesting to study the shape stability/instability of thin 2D materials against thermal fluctuations. In this paper, we study three types of surface models including Landau-Ginzburg (LG) and Helfirch-Polyakov models defined on triangulated hexagonal disks using the parallel tempering Monte Carlo simulation technique. We find that the planar surfaces undergo a first-order transition between the smooth and crumpled phases in the LG model and continuous transitions in the other two models. The first-order transition is relatively weak compared to the transition on spherical surfaces already reported. The continuous nature of the transition is consistent with the reported results, although the transitions are stronger than that of the reported ones. View Full-Text
Keywords: crumpling transition; graphene; graphene-based polymers; crumples; parallel tempering; Monte Carlo; statistical mechanics crumpling transition; graphene; graphene-based polymers; crumples; parallel tempering; Monte Carlo; statistical mechanics
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Shobukhov, A.; Koibuchi, H. Parallel Tempering Monte Carlo Studies of Phase Transition of Free Boundary Planar Surfaces. Polymers 2018, 10, 1360.

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