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We found that the order for the crumpling transition of an intrinsiccurvature model changes depending on the distance between two boundary verticesfixed on the surface of spherical topology. The model is a curvature onegoverned by an intrinsic curvature energy, which is defined on triangulatedsurfaces. It was already reported that the model undergoes a first-ordercrumpling transition without the boundary conditions on the surface. However,the dependence of the transition on such boundary condition is yet to bestudied. We have studied in this paper this problem by using the Monte Carlosimulations on surfaces up to a size N=8412. The first-order transition changesto a second-order one if the distance increases.

Phase transitions of a tethered membrane model with intrinsic curvature on spherical surfaces with point boundaries