Surface tension in an intrinsic curvature model with fixed one-dimensional boundaries

Abstract

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 the 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 τdiscontinuously changes. The gap of τremains constant at the transition point in a certain range of values A/N^\prime at sufficiently large N^\prime, which is the total number of vertices excluding the fixed vertices on the boundaries. The value of τremains almost zero in the wrinkled phase at the transition point while τremains negative finite in the smooth phase in that range of A/N^\prime.

12 pages, 8 figures

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