Large-scale structure of fluctuating order parameter field

An effective free energy for a fluctuating system is investigated using an exact (local) renormalization group (RG) equation. This equation accounts for the fluctuation interaction in a reduced manner (at Fisher exponent =0) and leads to a physical solution branch which gives realistic estimations for the free energy and nice critical exponents. It is shown that in spite of the monotonic character of the effective free energy in the critical region, all vertices should be taken into account in the effective Ginzburg-Landau-Wilson functional. The large-scale structure of the fluctuating field at a second-order phase transition is studied utilizing the calculated free energy and localized nonlinear excitations are found with profiles rather like those previously obtained in a model approach.