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The Ginzburg-Landau model with a Chern-Simons term is shown to possess two different scaling regimes depending on whether the mass of the scalar field is zero or not. In contrast to pure $\phi^4$ theories, the Ginzburg-Landau model with a topologically generated mass exhibits quite different properties in perturbation theory. Our analysis suggests that the two scalings could coincide at a non-perturbative level. This view is supported by a 1/N-expansion in the massive scalar field regime.

Two different scaling regimes in Ginzburg–Landau model with Chern–Simons term