Calculation of free energy of a three-dimensional Ising-like system in an external field with the use of the ρ6 model

The microscopic approach to calculating the free energy of a three-dimensional Ising-like system in a homogeneous external field is developed in the higher non-Gaussian approximation (the ρ6 model) at temperatures above the critical value of Tc (Tc is the phase-transition temperature in the absence of an external field). The free energy of the system is found by separating the contributions from the short- and long-wave spin-density oscillation modes taking into account both temperature and field fluctuations of the order parameter. Our analytical calculations do not involve power series in the scaling variable and are valid in the whole field–temperature plane near the critical point including the region in the vicinity of the limiting field h̃c, which divides external fields into the weak and strong ones (i.e., the crossover region).