Spherical surface models with directors

TL;DR

This study investigates a triangulated spherical surface model with a director field interaction, revealing phase transitions and demonstrating how the director interaction stabilizes the Nambu-Goto model, which is usually ill-defined.

Contribution

Introduces a novel surface model using director fields to maintain shape, contrasting with traditional curvature-based models, and shows it stabilizes the Nambu-Goto model.

Findings

The model exhibits phase transitions between smooth and collapsed states.

Director-surface interaction maintains surface shape without curvature energies.

The Nambu-Goto model becomes well-defined with the director interaction.

Abstract

A triangulated spherical surface model is numerically studied, and it is shown that the model undergoes phase transitions between the smooth phase and the collapsed phase. The model is defined by using a director field, which is assumed to have an interaction with a normal of the surface. The interaction between the directors and the surface maintains the surface shape. The director field is not defined within the two-dimensional differential geometry, and this is in sharp contrast to the conventional surface models, where the surface shape is maintained only by the curvature energies. We also show that the interaction makes the Nambu-Goto model well-defined, where the bond potential is given by the area of triangles; the Nambu-Goto model is well-known as an ill-defined one even when the conventional two-dimensional bending energy is included in the Hamiltonian.