Phase transitions in a fluid surface model with a deficit angle term

TL;DR

This study uses Monte Carlo simulations to explore phase transitions in a fluid surface model with a deficit angle term, revealing four distinct phases and spontaneous symmetry breaking.

Contribution

It demonstrates the existence of four phases and characterizes the nature of phase transitions in a fluid surface model with a deficit angle term.

Findings

Four distinct phases identified: crumpled, branched-polymer, linear, and tubular.

First-order transition observed between linear and tubular phases.

No long-range two-dimensional order or smooth surfaces in the model.

Abstract

Nambu-Goto model is investigated by using the canonical Monte Carlo simulation technique on dynamically triangulated surfaces of spherical topology. We find that the model has four distinct phases; crumpled, branched-polymer, linear, and tubular. The linear phase and the tubular phase appear to be separated by a first-order transition. It is also found that there is no long-range two-dimensional order in the model. In fact, no smooth surface can be seen in the whole region of the curvature modulus \alpha, which is the coefficient of the deficit angle term in the Hamiltonian. The bending energy, which is not included in the Hamiltonian, remains large even at sufficiently large \alpha in the tubular phase. On the other hand, the surface is spontaneously compactified into a one-dimensional smooth curve in the linear phase; one of the two degrees of freedom shrinks, and the other degree of freedom remains along the curve. Moreover, we find that the rotational symmetry of the model is spontaneously broken in the tubular phase just as in the same model on the fixed connectivity surfaces.