Calculation of thermodynamic functions of the three-dimensional Ising ferromagnet above and below critical temperature is performed in the approximation of sixfold basis distribution (ρ 6 model). Comparison with the results for the ρ 4 model indicates that dependence of the thermodynamic functions on the renormalization group parameter s becomes weaker. The optimal interval of the renormalization group parameter values is determined.

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 critical behaviour of the three-dimensional Ising-like system on a simple cubic lattice with an exponentially decreasing interaction potential is investigated within the collective variables method. The solution of the equation for the phase transition temperature is obtained by taking into account the dependence of its coefficients on the temperature. The dependence of the critical temperature on the interaction potential range is studied. 05.50.+q, 64.60.Fr, 75.10.Hk This paper gives rise into the theory of second order phase transitions in the approach developed by I.R.Yukhnovskii [1]. In a number of recent papers [2][3][4][5], the explicit expressions for basic thermodynamic functions of the three-dimensional Ising-like model have been obtained. In particular, the dependence of these functions on τ (τ = (T − T c )/T c , T c is the phase transition temperature), as well as on microscopic parameters of the model, was studied. On the other hand, the dependence of T c itself on microscopic parameters has not been studied deeply enough so far. Such a study is our aim in this research. Key words: Ising-like systems, critical behaviour, phase transitions, collective variables, phase transition temperature PACS:We investigate a system of Ising spins located at the sites of a simple cubic lattice L:The formal Hamiltonian of the system isHere h is an external field, r ij is the distance between the particles at the sites i and j, σ i is an operator of the z-component of a spin in the i-th site. The interaction

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.

The 3D one-component spin system in an external magnetic field is studied using the collective variables method. The integration of the partition function of the system over the phase space layers is performed in the approximation of the sextic measure density including the even and the odd powers of the variable (the asymmetric ρ 6 model). The general recurrence relations between the coefficients of the effective measure densities are obtained. The new functions appearing in these recurrence relations are given in the form of a convergent series.