Hausdorff dimension of critical fluctuations in abelian gauge theories

Details Hausdorff dimension of critical fluctuations in abelian gauge theories Hausdorff dimension of critical fluctuations in abelian gauge theories

2000-08-07

arxiv.org/abs/cond-mat/0008112v1

Phys.Rev.Lett. 85 (2000) 2368-2371

Physics

Condensed Matter

Superconductivity

Accepted for publication in PRL

Scientific paper

10.1103/PhysRevLett.85.2368

The geometric properties of the critical fluctuations in abelian gauge theories such as the Ginzburg-Landau model are analyzed in zero background field. Using a dual description, we obtain scaling relations between exponents of geometric and thermodynamic nature. In particular we connect the anomalous scaling dimension $\eta$ of the dual matter field to the Hausdorff dimension $D_H$ of the critical fluctuations, {\it which are fractal objects}. The connection between the values of $\eta$ and $D_H$, and the possibility of having a thermodynamic transition in finite background field, is discussed.

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