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Hausdorff dimension of critical fluctuations in abelian gauge theories

J. Hove·S. Mo·A. Sudbo
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Abstract

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 $η$ 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 $η$ and $D_H$, and the possibility of having a thermodynamic transition in finite background field, is discussed.

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J. Hove, S. Mo, A. Sudbo. 2000-08-07. Hausdorff dimension of critical fluctuations in abelian gauge theories. https://doi.org/10.1103/physrevlett.85.2368

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