24 research outputs found
The equation of state of a cell fluid model in the supercritical region
The analytic method for deriving the equation of state of a cell fluid model
in the region above the critical temperature () is
elaborated using the renormalization group transformation in the collective
variables set. Mathematical description with allowance for non-Gaussian
fluctuations of the order parameter is performed in the vicinity of the
critical point on the basis of the model. The proposed method of
calculation of the grand partition function allows one to obtain the equation
for the critical temperature of the fluid model in addition to universal
quantities such as critical exponents of the correlation length. The isothermal
compressibility is plotted as a function of density. The line of extrema of the
compressibility in the supercritical region is also represented.Comment: 26 pages, 6 figures, 1 tabl
Free Energy and Equation of State of Ising-like Magnet Near the Critical Point
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.Comment: 9 pages 2 figures in journal Nuclear physics B (in press but with
ref. v.753, pages 242-251
Analytical calculation of the critical temperature and estimation of the critical region size for a fluid model
An analytical procedure for calculating the critical temperature and
estimating the size of critical region for a cell fluid model is developed. Our
numerical calculations are illustrated by the case of the Morse potential
parameters characterizing the alkali metals (sodium and potassium). The
critical temperatures found for liquid sodium and potassium as solutions of the
resulting quadratic equation agree with experimental data. The expression for
the relative temperature determining the critical region size is obtained
proceeding from the condition for the critical regime existence. In the cases
of sodium and potassium, the value of this temperature is of the order of a few
hundredths.Comment: 15 pages, 2 table
3D Ising system in an external field. Recurrence relations for the asymmetric ρ⁶ model
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 ρ⁶ 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.Тривимірна однокомпонентна спінова система в зовнішньому магнітному полі досліджується з допомогою методу колективних змінних. Інтегрування статистичної суми системи по шарах фазового простору здійснюється в наближенні густини міри, яка містить в собі парні та непарні степені змінної до шостого включно (асиметрична модель ρ⁶). Одержано загальні рекурентні співвідношення між коефіцієнтами ефективних густин мір. Нові функції, що появляються в цих
рекурентних співвідношеннях, подані у вигляді збіжних рядів
Morse fluids in the immediate vicinity of the critical point: Calculation of thermodynamic coefficients
The previously proposed approach for the microscopic description of the
critical behavior of Morse liquids based on the cell fluid model is applied to
the case where the parameters of the Morse interaction potential correspond to
alkali metals (sodium and potassium). The critical temperatures, densities, and
pressures obtained for sodium and potassium agree with the experimental
results. The thermodynamic coefficients (isothermal compressibility, density
fluctuations, and thermal expansion) of sodium are investigated in the
supercritical temperature region. Numerical calculations of thermodynamic
coefficients are performed close to the critical point, where carrying out
theoretical and experimental research is challenging. The change in
compressibility with increasing density at various temperature values is
traced. The behavior of density fluctuations approaching the critical point is
shown for different temperatures. The variation in the magnitude of the thermal
expansion with increasing temperature for different pressure values is
illustrated.Comment: 14 pages, 6 figures, 1 tabl