2008/08/06 by Hiroshi Koibuchi
Engineering · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Curvature #Mean curvature #Monte Carlo method #Phase transition #Range (aeronautics) #Rigidity (electromagnetism) #Square (algebra) #Stochastic processes and statistical mechanics #Surface (topology) #Surface tension #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2008/08/p08008
published as Journal of Statistical Mechanics, (2008) P08008. · 12 pages, 8 figures
arxiv created 2008/08/06 · openalex publication_date 2008/08/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A triangulated fixed connectivity surface model is investigated by using the Monte Carlo simulation technique. In order to have the macroscopic surface tension τ, the vertices on the one-dimensional boundaries are fixed as the edges (= circles) of the tubular surface in the simulations. The size of the tubular surface is chosen such that the projected area becomes a regular square of area A . An intrinsic curvature energy with a microscopic bending rigidity b is included in the Hamiltonian. We found that the model undergoes a first-order transition of surface fluctuations at finite b , where the surface tension τ discontinuously changes. The gap of τ remains constant at the transition point in a certain range of values A / N ' at sufficiently large N ' , which is the total number of vertices excluding the fixed vertices on the boundaries. The value of τ remains almost zero in the wrinkled phase at the transition point while τ remains negative finite in the smooth phase in that range of A / N ' .