The behaviour of a three-dimensional magnet with a one-component order parameter near the critical point in a homogeneous external field is investigated. The calculations are performed in the case when the field and temperature are dependent and related by some expression (the system tends to the critical point along some trajectory). The high-and low-temperature regions in the vicinity of T c ( T c is the phase transition temperature in the absence of an external field) are considered. It is shown that in the weak fields the system behaviour is described in general by the temperature variable, but in the case of the strong fields the role of the temperature variable is not dominant. The corresponding expressions for the free energy, susceptibility and other characteristics of the system are obtained for each of these regions.

The effect of a homogeneous external field on the three-dimensional uniaxial magnet behaviour near the critical point is investigated within the framework of the nonperturbative collective variables method using the ρ 4 model. The research is carried out for the low-temperature region. The analytic explicit expressions for the free energy, average spin moment and susceptibility are obtained for weak and strong fields in comparison with the field value belonging to the pseudocritical line. The calculations are performed on the microscopic level without any adjusting parameters. It is established that the long-wave fluctuations of the order parameter play a crucial role in forming a crossover between the temperature-dependence and fielddependence critical behaviour of the system.

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A microscopic analogue of the Landau free energy for a three-dimensional one-component spin system is found below the critical temperature as a result of direct calculations. The obtained explicit expressions make it possible to analyse the dependence of coefficients of the analogue on temperature and microscopic parameters of the system. In contrast to the case for the Landau theory, the temperature dependence of these coefficients is nonanalytic. The quantities determining the coefficients in the expression for a microscopic analogue of the Landau free energy as well as the temperature-dependence curves for the order parameter of the system are given for different values of the effective radius of the exponentially decreasing interaction potential.

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