Thermodynamics of three-dimensional Ising-like systems in the higher non-Gaussian approximation: Calculational method and dependence on microscopic parameters

Behaviour of a Three-Dimensional Uniaxial Magnet Near the Critical Point in an External Field

“…The quantities F mτ +1 and F p form the contribution to the free energy F TR = F mτ +1 + F p , related with the transition region (TR). We separated this region when calculating the expression for the free energy at T > T c in the case of h = 0 (see [10,15]). The case of the weak fields (h <h c ) at T > T c requires to separate the TR as well.…”

Free energy and equation of state of Ising-like magnet near the critical point

“…In [16], the quantity ν = 0.643 is found for the similar approximation (the quartic potential but η = 0). As was shown in [17,18,19], the better convergent results within the approximation η = 0 can be obtained by using more complicated models. In particular, ν = 0.637, ν = 0.646 and ν = 0.649 for models ρ 6 , ρ 8 and ρ 10 , respectively [17].…”

“…As was shown in [17,18,19], the better convergent results within the approximation η = 0 can be obtained by using more complicated models. In particular, ν = 0.637, ν = 0.646 and ν = 0.649 for models ρ 6 , ρ 8 and ρ 10 , respectively [17]. The critical exponent of the correlation length for O(1) model calculated using Wegner-Houghton RG equation takes on the values 0.527, 0.586, 0.673 and 0.759 for the second, third, fourth and fifth order field truncations (corresponding to φ 4 , φ 6 , φ 8 and φ 10 ), respectively [20].…”

Recurrence relations for the three-dimensional Ising-like model in the external field

“…Explicit expressions for the partial partition functions Q n (3.15)-(3.17) are obtained. This allows us to calculate the free energy and other thermodynamic functions of the system near critical point by means of the methods of [2,8,9] . They will depend on the temperature and field and the form of these dependences as well as the corresponding critical exponents will be determined by the recurrence relations (3.19) and their solutions (4.22) near the fixed point (3.12).…”

“…The calculation of the non-universal quantities is connected with the use of non-Gaussian distributions in calculating the free energy [8,9], or with the use of some non-perturbative approach describing the critical properties of three-dimensional systems [10] accounting for the non-Gaussian fluctuations of the order parameter. The use of non-Gaussian distribution of fluctuations is especially important near the critical point of the second order phase transition for three-dimensional systems.…”