Microscopic description of the critical behavior of three-dimensional Ising-like systems in an external field

Kozlovskii, M. P.; Pylyuk, I. V.; Prytula, O. O.

doi:10.1103/physrevb.73.174406

Cited by 18 publications

(37 citation statements)

References 27 publications

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“…In additional to even powers of CV, the effective Hamiltonian has contained the odd part represented by the linear and cubic terms, which are related to the presence of the field. In contrast to the works [11,12], the present calculations are carried out without using power series in scaling variable. The size of the scaling region is a function of both the temperature and field variables.…”

Section: Introductionmentioning

confidence: 99%

“…At n > n p , due to changing the sign of the coefficient in the quadratic term in the exponent of relation (11), we can calculate the quantity I n+1 appearing in (6) on the basis of the Gaussian approximation. In the case of T > T c , the coefficient d np+1 increases gradually and, for the quantitative results, one should perform the additional step of integration [12]. Then the partition function (6) takes on the form…”

Section: The Case Of T > T Cmentioning

confidence: 99%

“…Using this method, we have already obtained thermodynamic characteristics in the form of a power series in the scaling variable in the regions of the weak and strong fields for temperatures above and below T c (T c is the phase transition temperature in the absence of an external field) [11,12]. In the mentioned papers as well as in [13], the size of the scaling region has been defined only by the temperature or by the field.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Kozlovskii¹,

Pylyuk²,

Prytula³

2006

Nuclear Physics B

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The description of a three-dimensional Ising-like magnet in the presence of an external field in the vicinity of the critical point by the collective variables method is proposed. Using the renormalization group transformations, the scaling region size is defined as a function of temperature and field. The obtained expressions for the free energy, equation of state and susceptibility allow one to analyse their dependence on microscopic parameters of the system. The critical exponents of the correlation length and order parameter are calculated as well. The results agree qualitatively with ones obtained within the framework of the parametric representation of the equation of state and Monte-Carlo simulations. The calculations do not involve any parametrization, phenomenological assumptions and adjustable parameters. The approach can be extended to models with a multicomponent order parameter.

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Section: Introductionmentioning

confidence: 99%

Section: The Case Of T > T Cmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Kozlovskii¹,

Pylyuk²,

Prytula³

2006

Nuclear Physics B

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“…The generalization to the case of "ϕ 6 "-model etc. one may perform by means of the results [11,13]. Concerning the function ϕ(ν l ) for simplicity we will use the first odd cumulant approximation, for which (1.23) holds.…”

Section: Representation Of the Partition Functionmentioning

confidence: 99%

“…The method for calculating the coefficients a n is given in [13]. The prime in the denotation of the coefficients a n indicates the use of the first odd cumulant approximation 1 .…”

Section: Representation Of the Partition Functionmentioning

confidence: 99%

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

Kozlovskii¹

2005

Condens. Matter Phys.

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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.

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Fluid critical behavior at liquid–gas phase transition: Analytic method for microscopic description

Pylyuk

2020

Journal of Molecular Liquids

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The behavior of fluids in the vicinity of the liquid-gas critical point is studied within the cell fluid model framework. The analytic method for deriving the equation of state of a cell fluid model in the low-temperature region (T < T c ) is developed using the renormalization group transformation within the collective variables approach. Mathematical description within the grand canonical ensemble is illustrated by an example of the Morse interaction potential possessing the Fourier transform. A specific feature of the proposed method lies in the possibility to use exclusively microscopic characteristics of a fluid (parameters of the interaction potential) for calculating macroscopic quantities (pressure and other thermodynamic quantities) without involving the hard-spheres reference system. The grand partition function, thermodynamic potential, and equation of state of the model near the critical point are derived taking into account the non-Gaussian (quartic) distribution of order parameter fluctuations. A nonlinear equation, which links the density and the chemical potential, is presented and solved. Graphs of the dependence of the density on the chemical potential are plotted for various values of the relative temperature. The numerical estimates of the critical-point parameters for potassium, obtained in addition to the estimates for sodium, are given. The calculated critical-point parameters for liquid alkali metals (sodium and potassium) are in accord with experimental data. The coexistence curve for sodium is plotted and compared with other authors' data in the immediate vicinity of T c , where theoretical and experimental researches are difficult to carry out. The differences between the obtained results and the earlier published results for T > T c are discussed.

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Microscopic description of the critical behavior of three-dimensional Ising-like systems in an external field

Cited by 18 publications

References 27 publications

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

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

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

Fluid critical behavior at liquid–gas phase transition: Analytic method for microscopic description

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