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O. A. Dobush

Publications and source records attributed to O. A. Dobush.

At least 19 recordsLinked to original sources

Thermodynamic response functions of the Curie-Weiss cell fluid model. I. Supercritical region

In this work, we present an analytical study of the thermodynamic response functions of a multiple-occupancy cell fluid model with competing Curie-Weiss attraction and local repulsion. In the grand canonical ensemble, explicit expressions are derived for the three independent response functions: the isothermal compressibility, the thermal pressure coefficient, and the isochoric heat capacity. The thermal expansion coefficient and the isobaric heat capacity are subsequently obtained from exact thermodynamic identities. The analytical formulas are used to investigate the behavior of the response functions in the supercritical region. The isothermal compressibility, the thermal expansion coefficient, and the isobaric heat capacity exhibit critical divergences, whereas the thermal pressure coefficient and the isochoric heat capacity remain finite at the critical points despite developing pronounced extrema. The thermal pressure coefficient displays a non-monotonic oscillatory dependence on density and becomes negative over a limited range of temperatures and densities, leading to negative values of the thermal expansion coefficient. The obtained analytical expressions provide a consistent theoretical framework for investigating the thermodynamic properties of the model and establish a basis for future analysis of the subcritical regime and multiphase equilibrium.

cond-mat.stat-mech

Phase diagram of a double-occupancy cell model of a fluid with Curie-Weiss interaction

A double-occupancy cell model of a fluid with Curie-Weiss interaction is studied. First, we show that the model is isomorphic to the Blume-Capel model on a complete graph through a simple transformation from spin to occupancy variables. We then investigate its phase behavior within the grand-canonical ensemble using a combination of analytical and numerical methods. Despite its simplicity, the model exhibits a remarkably rich thermodynamic behavior depending on the ratio between the local repulsive and global attractive interactions. We identify regimes characterized by a single critical point, two distinct critical points, tricritical behavior, and triple-point formation. For sufficiently strong repulsion, the system possesses three fluid phases of different densities, leading to both gas-liquid and liquid-liquid coexistence. The locations of the critical, tricritical, and triple points are determined, and the corresponding phase diagrams are constructed. These results demonstrate that the competition between double-occupancy repulsion and long-range attraction is sufficient to generate complex phase behavior in a minimal multiple-occupancy lattice-gas model.

cond-mat.stat-mech

The cell fluid model with Curie-Weiss interactions: special cases and analytical results

Inspired by previous extensive numerical studies of a cell fluid model with Curie-Weiss interactions, we concentrate on some analytically tractable special cases in its description. The key ingredient of the model is a competition between global attraction and local repulsion interactions between particles with coupling constants $J_1$ and $J_2$, respectively. We provide analytical results in several limiting cases, including the ideal-gas limit $J_1=J_2=0$ and the strong-repulsion limit $J_2\gg J_1$. For $J_2\gg J_1$, a detailed analytical study is presented. We derive explicit expressions for the critical point parameters, the equation of state, and the binodal and spinodal curves in closed form. The equation of state is found to be in full agreement with that of the van der Waals lattice gas, and the order parameter satisfies the standard Curie-Weiss equation. In a neighborhood of the critical point, a Landau expansion is shown to have the same form and symmetry as that of the classical lattice gas within the mean-field approximation. Moreover, based on the explicit knowledge of a few leading terms in the asymptotic expansion of the deformed exponential function governing the physics of the cell model, we extend its validity range to include the marginal case of thermodynamic stability, $J_1=J_2$. In particular, this extension makes a consideration of the ideal-gas limit $J_1=J_2=0$ formally legitimate. For the generic marginal case $J_1=J_2\ne0$ systematically avoided in previous works, we present numerical data and phase diagrams that augment their findings for $J_2>J_1$.

cond-mat.stat-mech

Triple point in a cell fluid model with effective temperature-dependent attraction

We study a cell fluid model of a many-particle system with Curie-Weiss-type interaction potential. It is considered as an open system in a fixed volume partitioned into a large number of congruent cubic cells. The interaction potential comprises two competing components: a global uniform attraction acting between all particle pairs in the volume and a short-range repulsion between particles occupying the same cell. Previous studies have established that this model admits an exact solution, exhibits multiple critical points, and undergoes a sequence of first-order phase transitions. Despite variations in the interaction strengths, no triple point appears as long as these parameters remain fixed. We demonstrate that incorporating effective {temperature-dependent} attractive interactions fundamentally alters the phase behavior of the cell model. This modification preserves the model's exact solvability while resulting in the emergence of a triple point in the phase diagram.

cond-mat.stat-mech

Entropy of the cell fluid model with Curie-Weiss interaction

Entropy of the cell fluid model with Curie-Weiss interaction is obtained in analytical form as a function of temperature and chemical potential. A parametric equation is derived representing the entropy as a function of density. Features of both the entropy per particle and the entropy per cell are investigated at the entropy-density and entropy-chemical potential planes. The considered cell model is a multiple-occupancy model and possesses an infinite sequence of first-order phase transitions at sufficiently low temperatures. We find that the entropy exhibits pronounced minima at around integer-valued particle densities, which may be a generic feature of multiple-occupancy models.

cond-mat.stat-mech

A multiple occupancy cell fluid model with competing attraction and repulsion interactions

An analytically solvable cell fluid model with unrestricted cell occupancy, infinite-range Curie-Weiss-type attraction and short-range intra-cell repulsion is studied within the grand-canonical ensemble. Building on an exact single-integral representation of the grand partition function, we apply Laplace's method to obtain asymptotically exact expressions for the pressure, density and equation of state. The model exhibits a hierarchy of first-order transitions, each terminating at a critical point. We determine the coordinates of the first five such points. Recasting the formalism in dimensionless variables highlights the explicit temperature dependence of all thermodynamic functions. This enables us to derive a closed-form expression for the entropy. The results reveal pronounced entropy minima around integer cell occupancies and reproduce density-anomaly isotherm crossings analogous to those in core-softened models.

cond-mat.stat-mech

Influence of attractive parts of interaction potentials on critical point parameters

We investigate how microscopic features of interparticle potentials influence macroscopic critical point parameters. Our analytical calculations are based on the cell model for continuous many-particle systems. We explore two types of pair interactions described by the Morse potential and a Curie-Weiss-type potential. For Morse fluids, we present numerical results obtained with microscopic parameters corresponding to the alkali metals sodium (Na) and potassium (K). The calculated dimensionless critical point parameters for liquid Na and K, expressed in dimensional units, allow for direct comparison with available experimental and simulation data. For the Curie-Weiss cell model with competing interactions, which exhibits a sequence of first-order phase transitions, we examine the critical parameters for the first three critical points. We analyze our results by varying the attractive part of the Morse potential and the Curie-Weiss attraction strength, providing insights into how these microscopic characteristics change critical point coordinates.

cond-mat.stat-mech

Influence of microscopic parameters on phase behavior of a cell model with Curie-Weiss interaction

We investigate how varying two microscopic parameters - cell volume and the ratio between repulsion and attraction intensities - affect the phase behavior of a cell model with a Curie-Weiss-type interaction. The analysis is based on an exact solution previously derived for this model in the grand canonical ensemble. At sufficiently low temperatures, the cell model exhibits multiple first-order phase transitions. By varying the cell volume and the repulsion-to-attraction ratio, we represent a quantitative comparison of the chemical potential and pressure isotherms, along with the pressure-temperature and temperature-density phase diagrams. Our results demonstrate that altering these microscopic parameters induces quantitative changes in the phase diagrams of the cell model.

cond-mat.stat-mech

A new special function related to a discrete Gauss-Poisson distribution and some physics of the cell model with Curie-Weiss interactions

Inspired by previous studies in statistical physics [see, in particular, Kozitsky at al., A phase transition in a Curie-Weiss system with binary interactions, Condens. Matter Phys. 23, 23502 (2020)] we introduce a discrete Gauss-Poisson probability distribution function \begin{equation}\label{GPD}\tag{A1} p_{GP}(n ;z,r)=\left[R(r;z)\right]^{-1}\frac{\mbox{e}^{zn}}{n!}\,\mbox{e}^{-\frac 12\,rn^2} \end{equation} with support on $\mathbb N_0$ and parameters $z\in\mathbb R$ and $r\in\mathbb R_+$. The probability mass function $p_{GP}(n ;z,r)$ is normalized by the special function $R(r;z)$, given by the infinite sum \begin{equation}\label{R}\tag{A2} R(r;z)=\sum_{n=0}^\infty\frac{\mbox{e}^{zn}}{n!}\,\mbox{e}^{-\frac 12\,rn^2}, \end{equation} possessing extremely intersting mathematical properties. We present an asymptotic estimate $R^{(\rm as)}(r;z\gg1)$ for the function $R(r;z)$ with large arguments $z$, along with similar formulas for its logarithm and logarithmic derivative. These functions exhibit very interesting oscillatory behavior around their asymptotics, for parameters $r$ above some threshold value $r^*$. Some implications of our findings are discussed in the context of the Curie-Weiss cell model of simple fluids.

cond-mat.stat-mech

Supercritical Crossover Lines in the Cell Fluid Model

A cell fluid model with a modified Morse potential is studied. The supercritical states are considered with respect to a possibility to build a separation boundary between liquid-like and gas-like bahaviors. Three different lines are calculated that can be used for this purpose: the locus of the isothermal compressibility maxima, the locus of the thermal expansion coefficient maxima, and the line where the effective chemical potential is zero, M=0. By the symmetry of the functionals for the partition functions, the condition M=0 in fluids is analogous to the absence of an external field in the Ising model.

cond-mat.stat-mech

Thermodynamic response functions in a cell fluid model

Thermodynamic response functions, namely the isothermal compressibility, the thermal pressure coefficient, and the thermal expansion coefficient, are calculated for a many-particle system interacting through a modified Morse potential. These calculations are based on an equation of state previously derived for a cell fluid model in the grand canonical ensemble. The calculated quantities are presented graphically as functions of density and the effective chemical potential.

cond-mat.stat-mech

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.

cond-mat.stat-mech

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.

cond-mat.stat-mech

Phase behavior of a cell model with Curie-Weiss interaction

The object of this study is a cell model with Curie-Weiss interaction potential. We have already proved the possibility of a mathematically rigorous transition from a continuous system of interacting particles to such a model and made an accurate calculation of its grand partition function. In the present research, we derive an explicit accurate equation of state of the cell model with Curie-Weiss potential. It turned out that this model has a sequence of first-order phase transitions at temperatures below the critical. We analyzed the mechanism of these transitions based on the behavior of the chemical potential as a function of density. Thus we found the points of phase coexistence without going beyond the microscopic approach. We also proposed a mathematically strict definition of the critical temperature as a function of the microscopic parameters of the model. We determined the parameters of the critical points and plotted phase diagrams which cover the area of the first three phase transitions in the sequence.

cond-mat.stat-mech

Equation of state of a cell fluid model with allowance for Gaussian fluctuations of the order parameter

The paper is devoted to the development of a microscopic description of the critical behavior of a cell fluid model with allowance for the contributions from collective variables with nonzero values of the wave vector. The mathematical description is performed in the supercritical temperature range ($T>T_c$) in the case of a modified Morse potential with additional repulsive interaction. The method, developed here for constructing the equation of state of the system by using the Gaussian distribution of the order parameter fluctuations, is valid beyond the immediate vicinity of the critical point for a wide range of density and temperature. The pressure of the system as a function of chemical potential and density is plotted for various fixed values of the relative temperature, both with and without considering the above-mentioned contributions. Compared with the results of the zero-mode approximation, the insignificant role of these contributions is indicated for temperatures $T>T_c$. At $T<T_c$, they are more significant.

cond-mat.stat-mech

Behavior of a binary asymmetric mixture of interacting particles in the supercritical region

We propose a method for describing a phase behavior of a system consisting of particles of two sorts. The interaction of each species is described by interaction potentials containing the repulsive and attractive components. Asymmetry is ensured by different values of the interaction potentials of each sort. The grand partition function of a binary mixture is calculated in the zero-mode approximation A line of critical points, which correspond to different proportions of the components, is calculated for specific values of parameters of the interaction potential. We have obtained an equation that relates the introduced mixing parameter x with the concentration of the fluid. An explicit expression of the pressure of the binary mixture is derived as a function of relative temperature and mixing parameter x to plot the Widom line. It is established that for boundary values of this parameter (x = 0 and x = 1), the equation of state of a mixture turns into equations of state of its separate species.

cond-mat.stat-mech

A phase transition in a Curie-Weiss system with binary interactions

A single-sort continuum Curie-Weiss system of interacting particles is studied. The particles are placed in the space $\mathbb{R}^d$ divided into congruent cubic cells. For a region $V\subset \mathbb{R}^d$ consisting of $N\in \mathbb{N}$ cells, every two particles contained in $V$ attract each other with intensity $J_1/N$. The particles contained in the same cell are subjected to binary repulsion with intensity $J_2>J_1$. For fixed values of the temperature, the interaction intensities, and the chemical potential the thermodynamic phase is defined as a probability measure on the space of occupation numbers of cells, determined by a condition typical of Curie-Weiss theories. It is proved that the half-plane $J_1\,\times\,$\textit{chemical potential} contains phase coexistence points at which there exist two thermodynamic phases of the system. An equation of state for this system is obtained.

math-ph