Phase transitions of a tethered surface model with a deficit angle term

TL;DR

This study uses Monte Carlo simulations to explore phase transitions in a tethered surface model with a deficit angle term, revealing three phases and symmetry breaking phenomena.

Contribution

It identifies and characterizes three distinct phases in the model, including a novel tubular phase with spontaneous symmetry breaking.

Findings

Three phases: crumpled, tubular, smooth

Crumpled and tubular phases are smoothly connected

Tubular and smooth phases are separated by a discontinuous transition

Abstract

Nambu-Goto model is investigated by using the canonical Monte Carlo simulations on fixed connectivity surfaces of spherical topology. Three distinct phases are found: crumpled, tubular, and smooth. The crumpled and the tubular phases are smoothly connected, and the tubular and the smooth phases are connected by a discontinuous transition. The surface in the tubular phase forms an oblong and one-dimensional object similar to a one-dimensional linear subspace in the Euclidean three-dimensional space R^3. This indicates that the rotational symmetry inherent in the model is spontaneously broken in the tubular phase, and it is restored in the smooth and the crumpled phases.