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

Abstract

The method for calculation of the partition function of lattice model for the magnet in the external field near critical point (CP) is proposed. The recurrence relations and their explicit solution near the critical point are founded. It is shown that dependence on temperature of thermodynamic functions near CP, when the field value comes down to zero, is in good agreement with the previous results obtained using the collective variable method. The phase transition temperature (when h = 0) is calculated and the dependence on parameters of interaction potential is found.

The order parameter and susceptibility of the 3D Ising-like system in an external field near the phase transition point

“…and expressions for a n have been obtained in [10]. Computation of (2.1) is performed by using the Kadanoff's idea of constructing block lattices [11,12].…”

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

“…In other words, the presence of the field caused to appearance of the additional relation for ω n in Eq. (14).…”

“…The coefficients γ, γ 1 , G 0 , t 2 and G 2 are independent of the field and are given in [14]. The quantity d n (B n+1 , B n ) = d n (0) + qs −2n is determined by the averaged Fourier transform of the interaction potential Φ(B n+1 , B n ) with the help of the relation…”

“…where quantities f 00 , α 2 , f 01 and α 4 are constants [14]. Performing the scaling transformations ρ k = sρ ′ k with introduction of the notations ω n = s n a…”

“…It should be noted, that the RR (13) and their solutions (14) are valid in the high-temperature region as well as in the case of T < T c at n ≤ n p .…”