Method Of Collective Variables Research Articles

On the role of atomic thermal vibrations in binary-alloy thermodynamics

An ab initio approach is advanced for the thermodynamical properties investigations of disordered binary alloys. Configurational and vibrational degrees of freedom are considered on the microscopic level in the grand partition sum calculations. Summing over the vibrational and configurational states of an alloy is performed within the reference system approach and the collective variables method, respectively. An equation defining the alloy free energy is obtained. The role of the atomic thermal vibrations in the binary-alloy thermodynamics and their relationship with the configurational effects are discussed. Conditions when the configurational and vibrational effects can be treated separately is formulated.

Connection of Landau-Ginsburg models with continuous microscopic approach for self-assembling systems

Abstract Studies of the self-assembling systems are usually carried out by (i) using microscopic lattice models or (ii) by exploring the Landau-Ginsburg density functionals (see e.g. [1]). In this work we try to link the connection between these approaches in a more general case of microscopic continuous Hamiltonian. We map this microscopic Hamiltonian onto a Landau-Ginsburg functional for self-assembling systems by using collective variables method (see e.g. [9]). We consider a three-component system which includes oil-like, water-like and surfactant molecules. Surfactant molecules could be modeled by two-types of water-like polar head and oil-like surfactant tail particles in a site-site description level or in the molecular level. In the atom-atom approach the so-called “charge frustrated” density functionals [6] are obtained; it is confirmed that taking into account the intra-molecular structure of surfactant molecules leads to Coulombic terms in the effective Hamiltonian. The connection of different types of Landau-Ginsburg Hamiltonians with the molecular-description level is discussed.

Determination of the Order Parameter in Binary Fluid Mixtures

We propose a microscopic approach to the study of phase transitions in fluid mixtures. It is based on the collective variables method with a reference system. The problem of definition of the order parameter in a two-component fluid system is considered in detail. This system is described with two sets of collective variables: ηk and ξk. It is shown that the CV connected with the order parameter is ηk=0 in the case of a gas–liquid critical point as well as in the case of a mixing–demixing phase transition. The relations between the microscopic parameters, temperature, density and concentration which determine the particular form of η0 for each of these phenomena are obtained. Based on these results we will be able to construct an effective Ginsburg–Landau–Wilson Hamiltonian.

3D ISING SYSTEM IN AN EXTERNAL FIELD. RECURRENCE RELATIONS FOR THE ASYMMETRIC \rho^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 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.

Determining Static Stresses of Deformed Solitons

An equation for the quasi-static soliton ansatz depending on an arbitrary set of collective variables is covariantly derived on the basis of the variational approach to the method of collective variables. The field configuration and the static stresses of the deformed $\Phi ^4$-kink that are produced by the excitation of the internal soliton mode are exactly determined. The kink interaction potential at large distances is considered for the example of the nonlinear Klein-Gordon system. A general approach to the problem of exactly determining the intersoliton potential for the entire set of physically admissible two-soliton configurations is discussed.

Thermodynamic characteristics of the classicaln-vector magnetic model in three dimensions

A method of calculating the free energy and thermodynamic characteristics of the classical n-vector three-dimensional magnetic model at the microscopic level without any adjustable parameters is proposed. Mathematical description is performed with the collective variables method used within the framework of the ${\ensuremath{\rho}}^{4}$ 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 analytical expressions for entropy, internal energy and 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 $Tg{T}_{c}$ and $Tl{T}_{c}$ on the microscopic parameters of the system are studied for the cases $n=1,2,3.$ The obtained results provide the basis for accurate analysis of the critical behavior in three dimensions including the nonuniversal characteristics of the system.

On the microscopic theory of phase transitions in binary fluid mixtures

The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order parameter in a binary mixture is discussed. The basic density measure (Ginzburg–Landau–Wilson Hamiltonian) is obtained in the collective variable phase space which contains the variable connected with the order parameter of the system. It is shown that the problem can be reduced to the 3D Ising model in an external field.

Critical behavior of the three-dimensional ising system: Dependence of thermodynamic characteristics on microscopic parameters

The results of investigating the critical behavior of the three-dimensional Ising model using the collective variables method are presented.

ATOMIC STATIC DISPLACEMENTS AND THEIR EFFECT ON THE SHORT RANGE ORDER IN ALLOYS

is obtained by the collective variables method. The theoretical results are illustrated by numerical calculations performed for disordered alloys of the K-Cs and Ca-Ba systems. A drastic effect of the ASD on the -function behaviour in the rst Brillouin zone is observed. The ASD smooth the dispersion of the -function. Negative values of the short-range order parameter on the rst coordination sphere indicate a trend to the ordering in alloys of the systems investigated. The ASD are shown to favour the ordering tendency. The theoretical conclusions concerning the temperature inuence on the short range order parameter perfectly agree with the experimental data from the treatment of the X-ray diffuse scattering in binary alloys.

Pancake-antipancake gas in layered superconductors

We consider the statistical mechanics of a layered superconductor in a magnetic field. The superconductor is described as a periodic system of superconducting layers coupled via a magnetic field. Each layer contains a gas of two-dimensional pancakes and antipancakes. To obtain the free energy of the pancake gas we used the method of collective variables which gives not only the main results of the Debye-H\uckel theory, but corrections to it as well. We have calculated the magnetization which shows all the main features of the reversible magnetization of high-temperature superconductors.

Investigation of the critical behaviour of n-component magnetic model

Investigation of the critical behaviour of the n-component three-dimentional (3D) magnetic model in the vicinity of the phase transition (PT) point is performed. Mathematical description based on the collective variables (CV) method. The universal characteristics of the system such as critical exponents and the critical amplitude ratios for thermodynamic functions above and below of the phase transition point are obtained, as well as non-universal ones. Calculation of the free energy in the ϱ 4 model at the microscopic level is performed. Explicit analytical expression for the heat capacity is obtained. It dependence on the microscopic parameters of the system and the component number n is analyzed. The main idea of present calculations is based on the systematic consideration of contributions of the short- and long-wavelength spin density fluctuations to the thermodynamic functions of the system. As the interaction potential we use an exponentially decreasing function of the distance between the particles.

On the Theory of Phase Transitions by the Collective Variables Methods

We calculate relatively accurate critical indices within the collective variables method applied to the phase transitions theory. Discussion on stability of the results and low-level comparison with the other approaches is made.

Critical phenomena in uniaxial ferroelectrics of order-disorder type

The description of critical phenomena in uniaxial cluster ferroelectrics of order-disorder type in the frames of the collective variables method is proposed. For a consistent integration a partition function functional in the neighbourhood of a phase transition point a non-Gaussian, quartic basic measure density of collective variables is used. A free energy of the system is obtained as a result of layer-by-layer integration. On the basis of calculated free energy the critical behaviour of investigated system is analyzed. It is shown, for example, that the heat capacity in the vicinity of Tc is proportional to In1/3 (T — Tc )/Tc .

Grand canonical distribution for multicomponent system in the collective variables method

The collective variables method with a reference system is developed for the case of the grand canonical ensemble for a multicomponent continuous system. The method is used to investigate phase transitions in a binary system. For a binary symmetrical system the relations between microscopic parameters determining the alternation of gas-liquid and separation phase transitions are found. The functional of the grand partition function of the symmetrical mixture is examined in the framework of parameters containing the separation point. The system is described with two sets of collective variables: ρk, a set connected with the gas-liquid critical point, andck, a set connected with the separation phenomenon. The fourfold basic density measure is constructed inck-variable phase space which contains the variablecv connected with the order parameter of the system. It is shown that the problem can be reduced to the 3D Ising model in an external field.

Molecular hydrodynamics of a weakly degenerate nonideal bose-gas II. Green functions and kinetic coefficients

The nonideal degenerate Bose-system at a temperature close to zero is investigated by N. N. Bogolyubov and D. N. Zubarev's method of collective variables. Applicable to a wide range of frequencies and wave vectors, interpolated expressions for the Green functions of the densities of conserved quantities and for the superfluid velocity potential are derived from exact relations. The criteria defining the validity domain of the hydrodynamic approximation are obtained. The kinetic coefficients of two-liquid hydrodynamics at temperatures close to zero are calculated for a weakly nonideal Bose-gas. A comparison with the method employing the kinetic equation for quasi-particles is made.

Investigation of a homogeneous many-particle system in the vicinity of the critical point

A theory based on a separate account of short-range repulsion and long-range attraction between particles is applied to the description of the liquid-gas critical point in the classical fluid case. The collective variables method with a reference system (RS) is used. Detailed investigation of the properties of RS cumulants makes it possible to transform the grand partition function into a functional form defined on the effective block lattice. The functional corresponds to the partition function of the Ising model in an external field. Then the collective variables method is used to calculate the Ising-model partition function in the vicinity of the phase transition point, which was developed in our previous papers. As a result one can separate reference system and long-range subsystem variables, which makes possible the quantitative solution of the liquid-gas critical point problem. The equation for the parameters of the critical point is obtained, as are explicit expressions for the equation of state both above and belowTc; the chemical potential of the system is investigated.

Theory of phase transitions by the collective variables method: accurate critical indices and detailed comparison with the other approaches

Theory of phase transitions by the collective variables method: accurate critical indices and detailed comparison with the other approaches

Investigation of phase transitions in binary systems by collective variables method

Investigation of phase transitions in binary systems by collective variables method

The partition sum of substitutional binary alloys within the collective variables method

The partition sum of substitutional binary alloys within the collective variables method

A description of the critical point of simple fluids in the collective variables method

A description of the critical point of simple fluids in the collective variables method