Is There a Glass Transition in Planar Vortex Systems?

The criteria for the existence of a glass transition in a planar vortex array with quenched disorder are studied. Applying a replica Bethe ansatz, we obtain for self-avoiding vortices the exact quenched average free energy and effective stiffness which is found to be in excellent agreement with recent numerical results for the related random bond dimer model [C. Zeng, P. L. Leath, and T. Hwa, Phys. Rev. Lett. 83, 4860 (1999)]. Including a repulsive vortex interaction and a finite vortex persistence length $\xi$, we find that for $\xi \to 0$ the system is at all temperatures in a glassy phase; a glass transition exists only for finite $\xi$. Our results indicate that planar vortex arrays in superconducting films are glassy at presumably all temperatures.

Figure 1

Replica Bethe ansatz result for the stiffness $K$, Eq. (9), plotted as function of the dimer temperature $T_d$, with ${\xi }_d=1.15$, and the corresponding data (circles) from the dimer model algorithm of Ref. 8.