10-06U

The critical behavior of the three-dimensional $n$-vector model in the presence of an external field is investigated. Mathematical description is performed with the collective variables (CV) method in the framework of the $\rho^4$ model approximation at the microscopic level without any adjustable parameters. The recurrence relations of the renormalization group (RG) as functions of the external field and temperature were found. The analytical expression for the free energy of the system for temperatures $T>T_c$ and different $n$ was obtained. The equation of state of the $n$-vector model for general case of small and large external fields was written. The explicit form of the correspondent scaling function for different values of the order parameter was derived. The obtained results are in qualitative agreement with the data of Monte Carlo simulations.