Shape transformation transitions of a tethered surface model

TL;DR

This study investigates a tethered surface model using Monte Carlo simulations, revealing multiple phase transitions and the absence of surface fluctuations in certain phases, enhancing understanding of surface behavior in statistical physics.

Contribution

It introduces a comprehensive analysis of phase transitions in a Nambu-Goto surface model with new phase classifications and transition characteristics.

Findings

Multiple distinct phases identified, including spherical, planar, linear, wormlike, and collapsed.

Almost all phase boundaries are characterized by discontinuous transitions.

Surface fluctuations are absent in spherical and planar phases.

Abstract

A surface model of Nambu and Goto is studied statistical mechanically by using the canonical Monte Carlo simulation technique on a spherical meshwork. The model is defined by the area energy term and a one-dimensional bending energy term in the Hamiltonian. We find that the model has a large variety of phases; the spherical phase, the planar phase, the long linear phase, the short linear phase, the wormlike phase, and the collapsed phase. Almost all two neighboring phases are separated by discontinuous transitions. It is also remarkable that no surface fluctuation can be seen in the surfaces both in the spherical phase and in the planar phase.