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R. V. Romanik

Publications and source records attributed to R. V. Romanik.

13 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

Microscopic description of the liquid-gas coexistence curve for Morse fluids in the immediate vicinity of the critical point

The present work is aimed at investigating the behavior of Morse fluids in the immediate vicinity of the critical point within the framework of a cell model. This region is of both fundamental and practical importance, yet presents analytical challenges due to the significant influence of order parameter fluctuations. An analytical procedure is developed to construct the upper part of the liquid-gas coexistence curve and calculate its diameter, incorporating the non-Gaussian (quartic) distribution of fluctuations. An explicit expression is derived for the temperature-dependent analytical term appearing in the expression for the rectilinear diameter. The numerical evaluation of the relevant quantities is carried out using Morse potential parameters representative of sodium. The coexistence curve is constructed both with and without the inclusion of the analytical temperature-dependent term in the calculation. A specific condition is identified under which the agreement between the presented binodal branches and Monte Carlo simulation data from other study, extrapolated to the immediate vicinity of the critical point, is improved. It is shown that better agreement is achieved when the analytical term is included in the calculation of the liquid branch and omitted in the gas branch. The proposed analytical approach may provide useful insight for the theoretical study of critical phenomena in more complex fluid systems.

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

A non-classical van der Waals loop: Collective variables method

The equation of state is investigated for an Ising-like model in the framework of collective variables method. The peculiar feature of the theory is that a non-classical van der Waals loop is extracted. The results are compared with the ones of a trigonometric parametric model in terms of normalized magnetization, \tilde{M}, and field, \tilde{H}.

cond-mat.stat-mech

Gibbs free energy and Helmholtz free energy for a three-dimensional Ising-like model

The critical behavior of a 3D Ising-like system is studied at the microscopic level of consideration. The free energy of ordering is calculated analytically as an explicit function of temperature, an external field and the initial parameters of the model. Within a unified approach, both Gibbs and Helmholtz free energies are obtained and the dependencies of them on the external field and the order parameter, respectively, are presented graphically. The regions of stability, metastability, and unstability are established on the order parameter-temperature plane. The way of implementation of the well-known Maxwell construction is proposed at microscopic level.

cond-mat.stat-mech