First-order phase transition of triangulated surfaces on a spherical core

We study an intrinsic curvature model defined on fixed-connectivity triangulated lattices enclosing a spherical core by using the canonical Monte Carlo simulation technique. We find that the model undergoes a discontinuous transition of shape transformation between the smooth state and a collapsed state even when the core radius R is sufficiently large; the transition depends on R. The origin of the multitude of transitions is considered to be a degeneracy of the collapsed states. We also find that the Gaussian bond potential S1/N, which is the sum of bond length squares, discontinuously changes at the transition. The discontinuity in S1/N implies a possibility of large fluctuations of the distance between lipids, or the density of lipids, in biological membranes such as giant vesicles or liposomes enclosing some materials.