Non-trivial effect of the in-plane shear elasticity on the phase transitions of fixed-connectivity meshwork models

TL;DR

This study reveals that in-plane shear elasticity significantly influences the phase transitions of fixed-connectivity surface models, strengthening surface fluctuation transitions and reducing phase variety.

Contribution

It demonstrates how in-plane shear elasticity alters phase transition behaviors and phase diversity in triangulated spherical surface models.

Findings

In-plane shear elasticity strengthens surface fluctuation transitions.

The presence of shear elasticity reduces the number of phases.

Models exhibit first-order collapsing transitions influenced by shear elasticity.

Abstract

We numerically study the phase structure of two types of triangulated spherical surface models, which includes an in-plane shear energy in the Hamiltonian, and we found that the phase structure of the models is considerably influenced by the presence of the in-plane shear elasticity. The models undergo a first-order collapsing transition and a first-order (or second-order) transition of surface fluctuations; the latter transition was reported to be of second-order in the first model without the in-plane shear energy. This leads us to conclude that the in-plane elasticity strengthens the transition of surface fluctuations. We also found that the in-plane elasticity decreases the variety of phases in the second model without the in-plane energy. The Hamiltonian of the first model is given by a linear combination of the Gaussian bond potential, a one-dimensional bending energy, and the in-plane shear energy. The second model is obtained from the first model by replacing the Gaussian bond potential with the Nambu-Goto potential, which is defined by the summation over the area of triangles.