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.
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
Integration is performed over collective variables in the partition function functional of the two-particle magnetic cluster system using the fourth basic measure density. To rigorously consider the Gaussian and the non-Gaussian fluctuations of the order parameter when dipole-dipole intercluster interactions take place, a two stage layer-by-layer method of integration is applied. To get the equation for the order parameter, the procedure of minimizing the integrand with the last (corresponding to zero values of quasimomentum and Matsubara's frequency) collective variable is used. Solutions of this equation in the phase transition point neighbourhood are found.
The problem of microscopic description of low-temperature phases in ferro-antiferroelectric mixed compounds is discussed. Those phases (ferro-, antiferroelectric and dipole glass) are interpreted based on the specific distributions for single and pair correlation functions in a non-ergodic thermodynamic system. Phase diagram and dielectric susceptibility of a mixed system are obtained and analyzed. : 75.10.Hk, 77.22.Ch, 77.84.F The recently introduced and analysed model [1,2] for microscopic investigation of ferroelectricantiferroelectric mixed compounds with hydrogen bonds predicts numerous solutions for single and pair correlation functions of interactive particles. The single correlation functions are directly connected with an order parameter (ferro-and antiferroelectric), but pair correlation functions describe a possible dipole glass phase and in its origin they are close to a well-known Edwards and Anderson spin glass parameter [3]. In the limit of small (n 0, 45) and large (n 0, 85) concentrations of ferroelectric component, the investigated system possesses antiferroelectric and ferroelectric properties up to the very low temperatures, respectively. However, for intermediate concentration (0, 45 < n < 0, 85) there arises a specific ordered phase with only short range correlations between particles. The number of different types of correlations (the number of different solutions for pair correlation functions) increase with temperature falling down [4]. Each of these pair correlation functions describe some specific arrangement of the nearest neighbours in disordered ferro-antiferroelectric systems. Since such systems are usually prepared due to high-speed cooling the distribution of such correlation functions is quite random. So, in order to calculate thermodynamic functions, the averaging procedure should be performed not for a partition function, as in Gibbs system, but for its logarithm, directly connected with the observed quantities. Key words: ferroelectrics, solid mixtures, phase diagram, dipole glass PACSOur approach differs from the well-known methods of investigating the mixed KDP-type compounds (see [5][6][7][8]). Those methods are based on the random fields taken into account, that are induced by competition between ferro-and antiferroelectric types of interaction in hydrogen bonds lattice. In this way, the dynamical properties of a mixed system were investigated too [9]. We have proposed a model of randomly distributed interacting groups (Rb-PO 4 and NH 4 -PO 4 ) which form a regular crystalline lattice. So, the microscopic proton-proton interactions are not considered directly. Such an approach essentially simplifies the calculations and provides good physical results.For rubidium ammonium dihydrogen phosphate -Rb n (NH 4 ) 1−n H 2 PO 4 (RADP) and isomorphous rubidium ammonium dihydrogen arsenate -Rb n (NH 4 ) 1−n H 2 AsO 4 (RADA) mixed compounds, this scheme of calculations (using replica method [10]) has shown the existence of at least two areas of different non-trivial solutions for ...
Neutron irradiation induced paramagnetic centers are investigated using EPR. It is shown that the observed EPR signal appears to be mainly due to a variety of radicals. Temperature dependence of the EPR linewidth is attempted to be correlated both with the results supplied by inelastic neutron scattering spectra and by the recently developed theoretical model for phase transitions in sodium ammonium sulphate dihydrate type crystals.
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