Renormalization of Fluctuating Tilted-Hexatic Membranes

TL;DR

This paper analyzes the phase transitions and critical behavior of fluctuating tilted-hexatic membranes using renormalization-group techniques, revealing multiple phases and transition mechanisms.

Contribution

It introduces a detailed renormalization-group analysis of tilted-hexatic membranes, identifying critical regions and phase transitions including crinkled-to-crumpled.

Findings

Identifies two critical regimes: strong and weak coupling.

Describes phase transitions involving disclinations and vortices.

Shows the crinkled phase's stiffness varies with coupling regime.

Abstract

We consider the tilted-hexatic Hamiltonian on the fluctuating membranes. A renormalization-group analysis leads us to find two critical regions; one corresponds to the strong coupling regime of the gradient cross coupling, the other to the weak coupling regime. In the strong coupling regime, we find the locked tilted-hexatic to liquid phase transition when disclinations and vortices unbind simultaneously. On the other hand, in the weak coupling regime we find four phases; the unlocked tilted-hexatic phase, the hexatic phase, the tilted phase, and liquid phase. Disclinations and vortices unbind independently. The crinkled-to-crumpled transition of the fluctuating tilted-hexatic membranes is also described. The crinkled phase in the strong coupling regime is stiffer than that in the weak coupling regime.