First-order phase transition in the tethered surface model on a sphere.

We show that the tethered surface model of Helfrich and Polyakov-Kleinert undergoes a first-order phase transition separating the smooth phase from the crumpled one. The model is investigated by the canonical Monte Carlo simulations on spherical and fixed connectivity surfaces of size up to N = 15 212. The first-order transition is observed when N > 7000, which is larger than those in previous numerical studies, and a continuous transition can also be observed on the smaller surfaces.

Phase transitions of a tethered surface model with a deficit angle term.

The Nambu-Goto model is investigated by using the canonical Monte Carlo simulations on fixed connectivity surfaces of spherical topology. Three distinct phases are found: crumpled, tubular, and smooth. The crumpled and the tubular phases are smoothly connected, and the tubular and the smooth phases are connected by a discontinuous transition.

First-order phase transition of fixed connectivity surfaces.

We report numerical evidence of the discontinuous transition of a tethered membrane model which is defined within a framework of the membrane elasticity of Helfrich. Two kinds of phantom tethered membrane models are studied via the canonical Monte Carlo simulation on triangulated fixed connectivity surfaces of spherical topology. One surface model is defined by the Gaussian term and the bending energy term, and the other, which is tensionless, is defined by the bending energy term and a hard wall potential.

Monte Carlo simulations of branched polymer surfaces without bending elasticity.

We study a model of elastic surfaces that was first constructed by Baillie et al. for an interpolation between the models of fluid and crystalline membranes. The Hamiltonian of the model is a linear combination of the Gaussian energy and a squared scalar curvature energy.