Exact solutions for correlation functions of an Ising nanocluster

Using a four-spin nanocluster as an example, a technique for developing exact expressions for correlation functions of Ising-type nanosystems is demonstrated. © 2009 Springer Science+Business Media, Inc

Langevin approach to the theory of dielectric relaxation of ice Ih

© 2018 Within the Langevin approach a new phenomenological model of dielectric relaxation of the ice is developed. This model is based on the concepts of defect migration, which is the main mechanism for dielectric relaxation of the ice. The new model allows to describe the relaxation behavior of the ice over a wide temperature range and to explain its characteristic features: changes in the slope of relaxation time at high and low temperatures (“crossovers”), and the non-monotonic temperature dependence of the broadening of dielectric loss peak parameter. The “crossover” of relaxation time at high temperatures is due to the transition from the predominant motion of the orientational defects of Bjerrum to the preferential motion of ionic defects with decreasing temperature and the weak correlation between them. On the contrary, at low temperatures a strongly correlated motion of ionic and orientational defects arises, which causes the observed low-temperature “crossover”

Study of magnetic ordering in a multisublattice Ising model in terms of static fluctuation approximation

In terms of the static fluctuational approximation previously developed by the authors, a closed set of equations was found for finding all necessary thermodynamic characteristics (including the calculation of two-particle correlation functions) of a multisublattice Ising model with an arbitrary interaction between spins over the entire temperature range. Magnetic ordering on a simple-cubic magnetic lattice is investigated with allowance for the nearest and next-nearest neighbors. Closed equations were obtained for binary correlation functions of a given system

Thermodynamic properties of electrons in quasi-periodic structures

© 2016 Author(s).The purpose of this study was investigating the specific heat properties of electrons in one dimensional quasiperiodic potentials. The electronic energy spectra were obtained from the monoscale Cantor set. The exact analytical results on the temperature dependence of the electron's specific heat associated with their fractal energy spectra are presented. A log-periodic behavior in low-temperature and nonoscillatory behavior in high-temperature regions was found for the specific heat. The exact value of the limiting temperature determining the boundary between these two regions was obtained

Magnetic properties of magnetoactive spin clusters

A simple model is proposed for describing magnetic properties of magnetoactive nanoclusters, which permits exact analytic solution. Exact expressions are obtained for thermodynamic characteristics of the model, which hold in the entire range of temperatures, magnetic fields, and interaction parameters. It is found that in the case of easy-axis anisotropy, the field dependence of magnetization of a nanocluster consisting of N particles with a spin of 1/2 has [N/2] fractional plateaus ([⋯] is the integer part) corresponding to polarized phases with ruptures singlet pairs. A nonmonotonic behavior observed for the magnetic susceptibility of an easy-plane cluster is typical of gap magnets. The spin gap between the ground state and excited states is proportional to the anisotropy parameter. © 2010 Pleiades Publishing, Ltd

Thermodynamics of Ising rare-earth magnet in the static fluctuation approximation

The authors obtain the closed self-consistent system of equations for calculation of the desired thermodynamic values of the Ising magnet with arbitrary spin and in presence of the single-ion anisotropy in the frame of the original static fluctuation approach (SFA). The essence of the SFA is based on accurate calculations of fluctuations of a molecular field. As an example the complete analysis of the critical behavior of the Ising magnet with spin S = 1 (Blume-Capiel model) is shown. The expressions for the phase transitions lines of the first and the second order are found. In addition, the coordinates of the tricritical point for some types of cubic lattices are found also. © 2014 Pleiades Publishing, Ltd

The NMR line shape of a system of nuclear spins with equal spin-spin coupling constants

We obtain an expression for the NMR line at low temperatures for a system of nuclear spins described by a Hamiltonian with equal spin-spin coupling constants. We show that in the case of "easy axis" anisotropy, the line has a logarithmic low-frequency singularity and an exponentially decreasing high-frequency asymptotic behavior at the temperature of an anomalous peak of heat capacity. In the case of "easy plane" anisotropy, the line has the traditional Gaussian form. We discuss the possibility of using NMR data to discover specific thermodynamic and magnetic properties of the considered model system. © 2011 MAIK/Nauka

Multiple-trapping model of dielectric relaxation of the ice I<inf>h</inf>

© 2017 Author(s). A microscopic theory of dielectric relaxation of the hexagonal ice (I h ) is proposed based on the multiple-trapping model. The theory explains the distinctive peculiarities of the relaxation time temperature behavior and the peak broadening parameter in a wide temperature range from the unified positions

Thermodynamic and magnetic properties of the finite spin complexes of the Ising type

In the frame of the static fluctuation approximation (SFA) the analysis of the thermodynamic and magnetic properties of the finite spin clusters in the 1D Ising model is performed It has been shown that under the influence of the magnetic impurity that forms the fixed value of the magnetization on the ends of spin complex the total magnetic ordering of the whole chain becomes possible. The results obtained in the frame of this model can open a way to understanding of magnetic properties of a wide class of the finite cluster systems. © 2014 Elsevier B.V

Ising model with competing axial interactions in the static fluctuation approximation

An original method, namely, the static fluctuation approximation (SFA) was used to study the thermodynamics of an Ising model with competing interactions between the nearest and next-nearest layers in the presence of an applied magnetic field. Three magnetically ordered phases (ferromagnetic, metamagnetic, and modulated) meeting at a multicritical point (the Lifshitz point) are shown to exist. Asymptotic expressions near the Lifshitz point for transition lines and the line of tricritical points are obtained. The modulated structure near the critical surface is shown to be a distorted sinusoidal wave with a period determined by the ratio γ of the competing interactions; in a zero magnetic field, only odd higher harmonics are present, whereas in a nonzero applied magnetic field, both even and odd harmonics exist. The nth-order harmonic asymptotically depends on the nth power of the fundamental harmonic. Expressions for correlation functions that correctly describe the modulated phase and exhibit characteristic oscillations are obtained