Approximate renormalization group transformation in the theory of phase transitions II. Equation for fixed points and linear operator of the renormalization group

The approximate renormalization group differential equation obtained earlier in a nonperturbative approach is linearized in the neighborhood of a fixed point. The explicit form is found for the system of equations for the fixed points of the renormalization group and the linear operator of the renormalization group whose spectrum determines the critical exponent. These expressions are representated in the form of expansions with respect to irreducible mean values of the field variables ($P$-expansions) calculated with respect to the distribution with complete free energy functional. The "$\varphi^4$" model is investigated.