Loop renormalization of the Ginzburg–Landau functional in the theory of phase transitions

For the free energy functional in the theory of phase transitions an expression is obtained that takes into account the loop renormalizations in all orders with respect to the $n$-component order parameter and in the first order in the vertices of the functional. It is shown, in particular, that such renormalizations cannot destroy the monotonicity of the functional and, therefore, lead to a phase transition of the first kind.