Critical phenomena in uniaxial ferroelectrics of order-disorder type

A two-stage layer by layer integration of the ferroelectric two-particle cluster system partition function functional is made in the quartic basic distribution of the dipole momentum fluctuation approximation. The shape of the layers of integration is determined by peculiarities of fluctuation processes (of the Gaussian and the non-Gaussian types) for separate subsets of collective variables. The minimization procedure of the partition function functional unintegrated over one variable (with quasimomentum and Matsubara's frequency equal to zero) gives an equation for the order parameter (i.e., the spontaneous polarization) of the system. Solutions of this equation at various values of system parameters and external field are found in the T c neighbourhood. Key words: functional, cluster ferroelectrics, phase transition, polarization PACS: 75.40.CxAmong various problems of investigating the real physical systems close to the phase transition point, namely calculating their universal and non-universal characteristics, the problem of the equation of state is a unique one. This is due to the fundamental role of such an equation for a complete description of thermodynamic properties of the system.The method of collective variables applied in the Ising model theory [1] has opened new possibilities in this area. The method enables us to provide a direct calculation of characteristic functions based on the equilibrium statistical physics.In the papers [2,3] an essential approach was made to obtain a free energy of the ferroelectric cluster system in the phase transition point neighbourhood. In order to obtain an equation of state (i.e., an equation for spontaneous polarization) it is necessary to integrate over all collective variables in the partition function functional with the exception of only one variable with momentum and Matsubara's frequency equal to zero. The mean value of this variable is, in fact, the order parameter of the c N.A.Korynevskii 631

mentioning

confidence: 99%

Spontaneous Polarization in the Cluster Ferroelectric System Close to the Phase Transition Point

Korynevskii¹

1999

“…Because the physical system considered in the present paper is described by a quantum Heisenberg-like Hamiltonian, the main features of its functional of the partition function are similar to the ones obtained in [7,10]. The principal difference in the form of functional coefficients is determined by the properties of the reference system.…”

Section: Functional Of the Partition Functionmentioning

confidence: 59%

“…For practical calculation of the expression (4.26), the layer by layer integration over collective variables ρ λ ( k, ν), similar to those exploited in [10,14], may be used. This problem is a subject of another paper.…”

Section: Heisenberg-type Intercluster Interactionsmentioning

confidence: 99%

See 1 more Smart Citation

On the Functional Representation of Partition Function for Quantum Magnetic Cluster Systems

Korynevskii¹

2002

The problem of the functional representation for systems containing groups of atoms with a non-compensated spin momentum (magnetic clusters) is discussed. For representation of the functional of partition function a version of the collective variables method with the "reference system" as a zero-order approximation is used. A set of all isolated clusters are choosen as a reference system. Intracluster interactions are described by exchange Heisenberg-type Hamiltonian, the form of intercluster interactions depend on the structure of the system investigated. Due to the use of the recently introduced generalized transition operators (like well-known HubbardStasyuk operators) an explicit form of the functional of partition function is found.

“…The present paper is a continuation of our recent investigations of ferroelectric-antiferroelectric mixed systems with hydrogen bonds [1][2][3]. There is an abundant experimental material concerning phase diagrams and the behaviour of thermodynamic functions for this mixed crystals [4][5][6][7][8].…”

mentioning

confidence: 99%

Ferroelectric-antiferroelectric mixed systems. Equation of state, thermodynamic functions

Korynevskii¹,

Solovyan²

2006

The problem of equation of state for ferroelectric-antiferroelectric mixed systems in the whole region of a concentration change (0 n 1) is discussed. The main peculiarity of the presented model turns out to be the possibility for the site dipole momentum to be oriented ferroelectrically in z-direction and antiferroelectrically in x-direction. Such a situation takes place in mixed compounds of KDP type. The different phases (ferro-, antiferro-, paraelectric, dipole glass and some combinations of them) have been found and analyzed. : 75.10.Hk, 77.22.Ch, 77.84.F The present paper is a continuation of our recent investigations of ferroelectric-antiferroelectric mixed systems with hydrogen bonds [1][2][3]. There is an abundant experimental material concerning phase diagrams and the behaviour of thermodynamic functions for this mixed crystals [4][5][6][7][8]. The phase diagrams demonstrate the coexistence of pure and mixed ferro-, antiferro-, paraelectric, dipole glass phases in a wide region of temperatures and concentrations. A theoretical description of such systems is in its initial stage so far. The main approach is based on the statistic replica method for calculating the thermodynamic functions for a mixed system with non-equilibrium distribution of differently occupied sites, similar to the ones exploited in mixed ferromagnetic system investigations [9]. Key words: ferroelectrics and antiferroelectrics, mixed systems, equation of state PACSIt is well known that short range interparticle interactions play an important role in ferroelectrics (especially in hydrogen bonded ones). So, in order to adequately describe the ferroelectricantiferroelectric mixed systems we should take into account both the short and long range interactions. An effective method was proposed in [2], where the model Hamiltonian includes two subsystems of particles with dipole momenta perpendicular to each other, with short and long range interaction between them and which depend on the probability of occupying each lattice site. In the second order of replica expansion for −βH (β = (kT ) −1 , k is the Boltzmann constant and T is the absolute temperature) the free energy of the system investigated has been obtained. The equations for ferroelectric P = S z , antiferroelectric ξ = S x order parameters and dipole glass g z = S z mi S z m i , g x = S x mi S x m i parameters were found. Here · · · denotes thermal averaging for a given distribution of z-and x-oriented dipole momenta of particles whereas a bar denotes a stochastic averaging over different distributions; m, m denotes the nearest neighbours of particles in i-th size. The obtained phase diagram (the temperature of the corresponding order parameter appearing versus concentration) shows a possibility of different phases occurring: ferro-, antiferro-, paraelectric, dipole glass and some combinations of them.The purpose of the present paper is to perform a continual study of ferroelectric-antiferroelectric mixed system taking into account the interaction processes between both subsys...