Vortex lines in the three-dimensional XY model with random phase shifts

TL;DR

This paper investigates the stability of the ordered phase in a 3D XY model with random phase shifts by analyzing vortex line roughening, confirming stability through theoretical and numerical methods.

Contribution

It introduces a novel analysis of vortex line roughening in disordered XY models, linking it to directed polymer theory and confirming stability criteria.

Findings

Roughness exponent estimated as ζ=3/4

Energy fluctuation exponent estimated as ω=1/2

Ordered phase remains stable due to ζ<1

Abstract

The stability of the ordered phase of the three-dimensional XY-model with random phase shifts is studied by considering the roughening of a single stretched vortex line due to the disorder. It is shown that the vortex line may be described by a directed polymer Hamiltonian with an effective random potential that is long range correlated. A Flory argument estimates the roughness exponent to $\zeta=3/4$ and the energy fluctuation exponent to $\omega=1/2$, thus fulfilling the scaling relation $\omega=2\zeta-1$. The Schwartz-Edwards method as well as a numerical integration of the corresponding Burger's equation confirm this result. Since $\zeta<1$ the ordered phase of the original XY-model is stable.