arXiv subjects

M. P. Kozlovskii

Publications and source records attributed to M. P. Kozlovskii.

33 records · Page 2Linked to original sources

arXiv2020

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↗

arXiv2019

Phase behavior of a cell fluid model with modified morse potential

The present manuscript gives a theoretical description of the first-order phase transition in a cell fluid model with a modified Morse potential and additional repulsive interaction. In the framework of the grand canonical ensemble, the equation of state of the system in terms of chemical potential-temperature and terms of density-temperature is calculated for a wide range of density and temperature. The behavior of the chemical potential as a function of temperature and density is investigated. The maximum and minimum admissible values of the chemical potential, which approach each other with decreasing temperature, are exhibited. The existence of a liquid-gas phase transition in a limited temperature range below the critical $T_c$ is established.

cond-mat.stat-mech↗

arXiv2018

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 ($T \geqslant T_\text{c}$) 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 $ρ^4$ 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.

cond-mat.stat-mech↗

arXiv2017

Using a fluid cell model for description of a phase transition in simple liquid alkali metals

This article embraces a theoretical description of the first order phase transition in liquid metals with application of a cell fluid model. The results are obtained through calculation of the grand partition function without usage of phenomenological parameters. The Morse potential is used for calculation of the equation of state and the coexistence curve. Specific results for sodium and potassium are obtained. Comparison of outcome of analytical expressions with data of computer simulations is presented.

cond-mat.stat-mech↗

arXiv2017

Phase transition in a cell fluid model

We propose a method of describing a phase transition in a cell fluid model with pair interaction potential that includes repulsive and attractive parts. An exact representation of the grand partition function of this model is obtained in the collective variables set. The behavior of the system at temperatures below and above the critical one is explored in the approximation of a mean-field type. An explicit analytic form of the equation of state which is applicable in a wide range of temperatures is derived, taking into account an equation between chemical potential and density. The coexistence curve, the surface of the equation of state and the phase diagram of the cell Morse fluid are plotted.

cond-mat.stat-mech↗

arXiv2013

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↗

arXiv2012

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↗

arXiv2010

The equation of state of the n-vector model: collective variables method

The critical behavior of the three-dimensional n-vector model in the presence of an external field is investigated. Mathematical description is performed with the collective variables (CV) method in the framework of the $ρ^4$ model approximation at the microscopic level without any adjustable parameters. The recurrence relations of the renormalization group (RG) as functions of the external field and temperature were found. The analytical expression for the free energy of the system for temperatures $T>T_c$ and different n was obtained. The equation of state of the n-vector model for general case of small and large external fields was written. The explicit form of the correspondent scaling function for different values of the order parameter was derived. The obtained results are in qualitative agreement with the data of Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2008

Method of Calculating the Free Energy of Three-Dimensional Ising-Like System in an External Field with the Use of the $ρ^6$ Model

The microscopic approach to calculating the free energy of a three-dimensional Ising-like system in a homogeneous external field is developed in the higher non-Gaussian approximation (the $ρ^6$ model) at temperatures above the critical value of $T_c$ ($T_c$ is the phase-transition temperature in the absence of an external field). The free energy of the system is found by separating the contributions from the short- and long-wave spin-density oscillation modes taking into account both the temperature and field fluctuations of the order parameter. Our analytical calculations do not involve power series in the scaling variable and are valid in the whole field-temperature plane near the critical point including the region in the vicinity of the limiting field $\tilde h_c$, which divides external fields into the weak and strong ones (i.e., the crossover region). In this region, the temperature and field effects on the system are equivalent, the scaling variable is of the order of unity, and power series are not efficient. The obtained expression for the free energy contains the leading terms and terms determining the temperature and field confluent corrections.

cond-mat.stat-mech↗

arXiv2006

Equation of State and Thermodynamic Functions of the Ising-like Magnet at $T>T_c$

The 3D Ising-like system in the external field is described using the non-perturbative collective variables method. The universal as well as nonuniversal system characteristics are obtained within the framework of this approach. The calculations are carried out on the microscopic level starting from the Hamiltonian. They are valid in the whole $h-T$ plane of the critical region. It is established, that the contributions related with wave vector values $\vk\to0$ exhibit the properties of the total system near the critical point. The behaviour of the susceptibility as function of the temperature in the presence of the field is investigated. The locations of the maximums susceptibility on the temperature scale for different values of the field are established.

hep-th↗

arXiv2006

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.

hep-th↗

arXiv2001

3D Ising System in an External Field. Recurrence Relations for the Asymmetric $ρ^6$ 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 $ρ^6$ 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.

cond-mat.stat-mech↗

arXiv1999

Calculation Method for the Three-Dimensional Ising Ferromagnet Thermodynamics within the Frames of $ρ^6$ Model

Calculation of thermodynamic functions of the three-dimensional Ising ferromagnet above and below critical temperature is performed in the approximation of sixfold basis distribution ($ρ^6$ model). Comparison with the results for the $ρ^4$ model indicates that dependence of the thermodynamic functions on the renormalization group parameter $s$ becomes weaker. The optimal interval of the renormalization group parameter values is determined.

cond-mat.stat-mech↗

arXiv1999

Ab initio study of the vapour-liquid critical point of a symmetrical binary fluid mixture

A microscopic approach to the investigation of the behaviour of a symmetrical binary fluid mixture in the vicinity of the vapour-liquid critical point is proposed. It is shown that the problem can be reduced to the calculation of the partition function of a 3D Ising model in an external field. For a square-well symmetrical binary mixture we calculate the parameters of the critical point as functions of the microscopic parameter r measuring the relative strength of interactions between the particles of dissimilar and similar species. The calculations are performed at intermediate ($λ=1.5$) and moderately long ($λ=2.0$) intermolecular potential ranges. The obtained results agree well with the ones of computer simulations.

cond-mat↗

arXiv1998

Thermodynamic characteristics of the classical n-vector magnetic model in three dimensions

The method of calculating the free energy and thermodynamic characteristics of the classical n-vector three-dimensional (3D) magnetic model at the microscopic level without any adjustable parameters is proposed. Mathematical description is perfomed using the collective variables (CV) method in the framework of the $ρ^4$ model approximation. The exponentially decreasing function of the distance between the particles situated at the N sites of a simple cubic lattice is used as the interaction potential. Explicit and rigorous analytical expressions for entropy,internal energy, specific heat near the phase transition point as functions of the temperature are obtained. The dependence of the amplitudes of the thermodynamic characteristics of the system for $T>T_c$ and $T<T_c$ on the microscopic parameters of the interaction potential are studied for the cases $n=1,2,3$ and $n\to\infty$. The obtained results provide the basis for accurate analysis of the critical behaviour in three dimensions including the nonuniversal characteristics of the system.

cond-mat.stat-mech↗