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An analytic method for deriving the free energy of a three-dimensionalIsing-like system near the critical point in a homogeneous external field isdeveloped in the $\rho^6$ model approximation. The mathematical descriptionproposed for temperatures $T>T_c$ ($T_c$ is the phase-transition temperature inthe absence of an external field) is valid for fields near $\tilde h_c$, wherethe scaling variable is of the order of unity and power series in this variableare not effective. At the limiting field $\tilde h_c$, the temperature andfield effects on the system in the vicinity of the critical point areequivalent. The total free energy is obtained as a function of temperature,field and microscopic parameters of the system without using series expansionsin the scaling variable. In addition to leading terms, the expression for thefree energy includes the terms determining the temperature and field confluentcorrections.

Three-Dimensional Ising-Like System in an External Field: Microscopic Calculation of the Free Energy in the Higher Non-Gaussian Approximation