Anomalous scaling dimensions and critical points in type-II superconductors
Abstract
The existence of a stable critical point, separate from the Gaussian and XY critical points, of the Ginzburg-Landau theory for superconductors, is demonstrated by direct extraction via Monte-Carlo simulations, of a negative anomalous dimension ηφ of a complex scalar field φ forming a dual description of a neutral superfluid. The dual of the neutral superfluid is isomorphic to a charged superfluid coupled to a massless gauge-field. The anomalous scaling dimension of the superfluid order-field is positive, while we find that the anomalous dimension of the dual field is negative. The dual gauge-field does not decouple from the dual complex matter-field at the critical point. These two critical theories represent separate fixed points. The physical meaning of a negative ηφ is that the vortex-loop tangle of the superfluid at the critical point fills space more efficiently than random walkers, without collapsing. This is due to the presence of the massless dual gauge-field, and the resulting long-ranged vectorial Biot-Savart interaction between vortex-loop segments, which is a relevant perturbation to the steric | ψ| 4 repulsion term. Hence, the critical dual theory is not in the universality class of the | ψ| 4-theory.
- Publication:
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Physica B Condensed Matter
- Pub Date:
- May 2000
- DOI:
- 10.1016/S0921-4526(99)01571-9
- arXiv:
- arXiv:cond-mat/9907386
- Bibcode:
- 2000PhyB..280..194S
- Keywords:
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- Condensed Matter - Superconductivity
- E-Print:
- 2 pages, 1 figure