Phase Diagrams for Deformable Toroidal and Spherical Surfaces with Intrinsic Orientational Order

TL;DR

This paper presents a theoretical analysis of toroidal membranes with intrinsic orientational order, revealing complex phase behavior, including various ordered states, phase transitions, and the formation of vortex structures.

Contribution

It introduces a mean-field Ginzburg-Landau model for toroidal membranes, uncovering novel phases and phenomena not previously characterized.

Findings

Multiple phases with continuous and first-order transitions

Spontaneous symmetry breaking and vortex-antivortex formations

Phase diagrams showing transitions between different toroidal and spherical states

Abstract

A theoretical study of toroidal membranes with various degrees of intrinsic orientational order is presented at mean-field level. The study uses a simple Ginzburg-Landau style free energy functional, which gives rise to a rich variety of physics and reveals some unusual ordered states. The system is found to exhibit many different phases with continuous and first order phase transitions, and phenomena including spontaneous symmetry breaking, ground states with nodes and the formation of vortex-antivortex quartets. Transitions between toroidal phases with different configurations of the order parameter and different aspect ratios are plotted as functions of the thermodynamic parameters. Regions of the phase diagrams in which spherical vesicles form are also shown.