A three-dimensional Ising-like system in a homogeneous external field is
studied on the basis of the higher non-Gaussian measure density (the

The Ising model is one of the most studied models in the theory of the phase transitions, not only because it is considered as the prototype of statistical systems showing a nontrivial power-law critical behaviour, but also because it describes several physical systems [

The description of the phase transitions in the

The free energy of a

The present paper supplements the earlier works [

Evolution of the critical exponent of the correlation length

Saturation of the critical exponent

The methods existing at present make it possible to calculate universal quantities to a quite high degree of accuracy (see, e.g., [

The expressions for the thermodynamic characteristics of the system in the presence of an external field have already been obtained on the basis of the simplest non-Gaussian measure density (the

We consider a

In the CV representation for the partition function of the system, we have [

Proceeding from (

The integration over the zeroth, first, second,

Quantities, which characterize the coordinates of the fixed point.

0.5668 | 0.5647 | 0.4870 | 1.0000 | 1.7576 | 2.6740 |

Let us calculate the free energy

A calculation technique based on the

Having expression (

The eigenvalues

12.3695 | 4.8468 | 0.4367 | 0.0032 | 0.637 | 0.525 | 3.647 |

We shall perform the further calculations on the basis of (

Proceeding from an explicit dependence of

Let us now calculate the contribution to the free energy of the system from the layers of the CV phase space beyond the point of exit from the critical regime region. The calculations are performed according to the scheme proposed in [

This region corresponds to

The free energy contribution

The basic arguments in the (

Dependence of quantities

Power series in small deviations

Proceeding from expression (

The final result for

Let us now calculate the contribution to the free energy of the system from long-wave modes in the range of wave vectors

The free energy component

Introducing the designation

Taking into account (

Relations (

On the basis of (

The total free energy of the system is calculated taking into account (

The advantage of the method presented in this paper is the possibility of deriving analytic expressions for the free-energy coefficients as functions of the microscopic parameters of the system (the lattice constant

A

An initial expression for the partition function of the system is constructed in the form of a functional with explicitly known coefficient functions [see (

The main distinctive feature of the presented method for calculating the total free energy of the system is the separate inclusion of the contributions to the free energy from the short- and long-wave spin-density oscillation modes. The expression for the generalized point of exit of the system from the critical regime contains both the temperature and field variables. The form of the temperature and field dependences for the free energy of the system is determined by solutions of RR near the fixed point.

The expression for the free energy