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

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.

8 pages RevTeX, 3 eps-figures included

References in corpus (2)

• Topological Defects in the Random-Field XY Model and the Pinned Vortex Lattice to Vortex Glass Transition in Type-II Superconductors
• Vortex statistics in a disordered two-dimensional XY model

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• Asymptotic Matching the Self-Consistent Expansion to Approximate the Modified Bessel Functions of the Second Kind