Shape Transformations of Triangulated Spherical Surfaces in Parallel Plates

Abstract

We numerically study a spherical surface model and find that the model undergoes a shape transformation between the pancake phase and the concave phase. A constraint potential included in the Hamiltonian confines the surface inside a couple of parallel plates. The Hamiltonian including the Gaussian bond potential and the extrinsic curvature energy is discretized on fixed-connectivity triangulated surfaces, which are allowed to self-intersect. The shape transformation between the pancake phase and the concave phase occurs at relatively large bending rigidity b, where the surface is quite smooth and hence self-avoiding. This transformation is considered to be a phase transition because the size fluctuation follows to a scaling relation typical to the continuous transition, although the curvature energy remains almost constant against b at the transition region.