CALCULATION METHOD FOR THE THREE-DIMENSIONAL ISING FERROMAGNET THERMODYNAMICS WITHIN THE FRAMES OF rho^{6} MODEL

Kozlovskii, M. P.; Pylyuk,; Dukhovii,

doi:10.5488/cmp.11.17

Cited by 15 publications

(39 citation statements)

References 13 publications

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“…The present paper supplements the earlier works [8][9][10][11], in which the ρ 6 model was used for calculating the free energy and other thermodynamic functions of the system in the absence of an external field. The ρ 6 model provides a better quantitative description of the critical behaviour of a 3D Ising-like magnet than the ρ 4 model [10].…”

Section: Introductionsupporting

confidence: 63%

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Free Energy of Three-Dimensional Uniaxial Magnet in the Higher Non-Gaussian Approximation and in the Presence of an External Field

Kozlovskii

Pylyuk

2011

ISRN Condensed Matter Physics

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A three-dimensional Ising-like system in a homogeneous external field is studied on the basis of the higher non-Gaussian measure density (the ρ 6 model). The presented solutions of recurrence relations for the coefficients of the effective measure densities and the generalized point of exit of the system from the critical regime are used for calculating the free energy of the system at temperatures T > T c (T c is the phase transition temperature in the absence of an external field). A calculation technique is based on the first principles of statistical physics and is naturally realized without any general assumptions and without any adjustable parameters. The obtained expression for the free energy does not involve series expansions in the scaling variable and is valid near the critical point not only in the regions of the so-called weak and strong external fields, but also in the crossover region between these fields, where power series in the scaling variable are not effective.

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Section: Introductionsupporting

confidence: 63%

“…The expressions for the remaining coefficients are given in [8][9][10][11]. These coefficients are functions of s 0 , that is, of the ratio of microscopic parameters b and c. We shall use the method of "layerby-layer" integration of (6) with respect to variables ρ k described in [2][3][4].…”

Section: General Relationsmentioning

confidence: 99%

Free Energy of Three-Dimensional Uniaxial Magnet in the Higher Non-Gaussian Approximation and in the Presence of an External Field

Kozlovskii

Pylyuk

2011

ISRN Condensed Matter Physics

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“…The methods existing at present make it possible to calculate critical characteristics to a quite high degree of accuracy (see, for example [17,18]). The advantage of the method under investigation lies in the possibility to obtain and analyze expressions for thermodynamic characteristics and their amplitudes as functions of microscopic parameters of the system [2][3][4][5]19]. It is shown (see, for example, [2,4,20,21]) that the leading critical amplitudes and the correction-to-scaling amplitudes for the specific heat, average spin moment, susceptibility of the system can be presented in the form of the product of the universal part, independent of microscopic parameters, and the nonuniversal factor, which depends on these parameters.…”

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confidence: 99%

Dependence of the Critical Temperature on Microscopic Parameters in the Three-Dimensional Ising-Like Systems

Kozlovskii¹,

Dukhovii²,

Pylyuk³

2000

Condens. Matter Phys.

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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

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“…The confinement to the 6th power of the CV in the expression for a measure density corresponds to the ρ 6 model. This model provides a more adequate quantitative description of the 3D Ising system behaviour in comparison with the ρ 4 model (see [7][8][9]). …”

Section: Introductionmentioning

confidence: 99%

“…In our earlier works (see, for example, [7][8][9]), an infinitely weak external field was introduced in the course of calculation of the contribution from the long-wave modes of the spin moment density oscillations to the 3D Ising system thermodynamic characteristics. In this paper, we introduce an external field in the Hamiltonian from the outset.…”

Section: Introductionmentioning

confidence: 99%

3D ISING SYSTEM IN AN EXTERNAL FIELD. RECURRENCE RELATIONS FOR THE ASYMMETRIC \rho^6 MODEL

Pylyuk¹,

Kozlovskii²

2001

Condens. Matter Phys.

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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.

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CALCULATION METHOD FOR THE THREE-DIMENSIONAL ISING FERROMAGNET THERMODYNAMICS WITHIN THE FRAMES OF rho^{6} MODEL

Cited by 15 publications

References 13 publications

Free Energy of Three-Dimensional Uniaxial Magnet in the Higher Non-Gaussian Approximation and in the Presence of an External Field

Free Energy of Three-Dimensional Uniaxial Magnet in the Higher Non-Gaussian Approximation and in the Presence of an External Field

Dependence of the Critical Temperature on Microscopic Parameters in the Three-Dimensional Ising-Like Systems

3D ISING SYSTEM IN AN EXTERNAL FIELD. RECURRENCE RELATIONS FOR THE ASYMMETRIC \rho^6 MODEL

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