Wavelet-induced renormalization group for the Landau-Ginzburg model

The scale hierarchy of wavelets provides a natural frame for renormalization. Expanding the order parameter of the Landau-Ginzburg/${\mathrm{\Phi }}^4$ model in a basis of compact orthonormal wavelets explicitly exhibits the coupling between scales that leads to non-trivial behavior. The locality properties of Daubechies’ wavelets enable us to derive the qualitative renormalization flow of the Landau-Ginzburg model from Gaussian fluctuations in wavelet space.