Do 1+1 Dimensional Vortex Systems show a Glass Transition?
Abstract
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 a related random bond dimer model. Including a repulsive vortex interaction and a finite vortex persistence length ξ, we find that for ξ arrow 0 the system is at all temperatures in a glassy phase; a glass transition exists only for finite ξ. The shortcomings of the standard mapping to the random field XY (RFXY) model, which does undergo a transition for any ξ, are explained and the free energy of the RFXY model is shown to be analytical at the transition. Our results indicate that planar vortex arrays in superconducting films are glassy at presumably all temperatures. Comparison of our predictions with latest high accuracy numerical computations by Zeng et al., which are also presented at this conference, both confirms strikingly the Bethe ansatz results above and also sheds new light on the long standing problem of a single elastic polymer in a random environment.
- Publication:
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APS March Meeting Abstracts
- Pub Date:
- March 2003
- Bibcode:
- 2003APS..MARY32008B