Totally symmetric order parameter in the framework of the phenomenological theory of phase transitions: Ferroelastics

A new approach is proposed for constructing the phenomenological theory of phase transitions. The approach is based on the classical Landau theory with allowance made for the order parameter that corresponds to changes in the charge distribution probability density of a crystal and does not affect the symmetry of the high-symmetry phase. It is demonstrated that this approach makes it possible to describe phase transitions in terms of a nonequilibrium polynomial Landau potential of degree four in the components of the order parameters. The capabilities of the proposed approach are illustrated with three systems that undergo ferroelastic phase transitions.     

威耳逊的临界点相变的重正化群理论

临界现象的研究进展缓慢,６０年代实验方面的发展使人们相继建立了几个标度理论及普适性理论,并提出了标度变换概念,威耳逊一直从事量子场论的研究,对相变理论也很关注,对迹些唯象理论不满,他把量子场论中的重正化群概念应用到相变理论中,并运用标度律和普适性概念,建立了临界点的重点重正化群理论,提供了研究临界点现象的系统方法。     

Toward the theory of quantum phase transitions in DTN-type van Vleck antiferromagnets

A magnetic field-induced singlet-to-antiferromagnetic quantum magnetic phase transition has been considered. It has been shown that the phenomenon can be described within an approach similar to the Landau theory of phase transitions. The case of an oblique magnetic field has been studied and the critical field-angle phase diagram has been determined. The phase diagram agrees with the experimental one observed in DTN.     

Stable spiral domains in ferrite-garnet films

Stable spiral domain structures—spiral domains stabilized by a bubble lattice and lattices of spiral domains—in epitaxial ferrite-garnet films have been experimentally investigated. The thermodynamic approach based on the concept of magnetostatic pressure is applied to explain the behavior of a spiral domain structure with a change in temperature or magnetic field. It is shown that phase transitions in spiral domains are related to phase transitions in the bubble lattice.     

Fluctuating field near spinodal

Phase ordering kinetics with a non-conserved scalar order parameter is studied near a lability boundary of a first-order phase transition. A large-scale structure of this field is found to appear. Under some conditions it is analogous to a fractal structure in the critical region of a second-order transition. The chains and localized groups of new phase nuclei are generated by the maxima of the order parameter density. The results are compared with fluctuation inducing of continuous phase transitions predicted in the framework of the renormalization group (RG) approach.     

Orientational Ordering of a Liquid-Crystal Suspension of Carbon Nanotubes in a Magnetic Field

A statistical theory is proposed to describe a suspension of carbon nanotubes in a nematic liquid crystal. The mean-field approach is used, and dispersion attraction, the excluded volume effects, the diamagnetism of liquid crystal molecules, and the strong diamagnetism of nanotubes are taken into account. The influence of the volume fraction of impurity, temperature, and magnetic field on the orientational ordering of a liquid crystal matrix and carbon nanotubes is studied. The concentration and temperature phase transitions in the suspension are investigated for various magnetic fields. The concentration and field shifts of the point of the phase transition between nematic and isotropic or paranematic phases are studied.     

The quantum compass chain in a transverse magnetic field

We study the magnetic behaviors of a spin-1/2 quantum compass chain (QCC) in a transverse magnetic field, by means of the analytical spinless fermion approach and numerical Lanczos method. In the absence of the magnetic field, the phase diagram is divided into four gapped regions. To determine what happens by applying a transverse magnetic field, using the spinless fermion approach, critical fields are obtained as a function of exchanges. Our analytical results show, the field-induced effects depend on in which one of the four regions the system is. In two regions of the phase diagram, the Ising-type phase transition happens in a finite field. In another region, we have identified two quantum phase transitions (QPT)s in the ground state magnetic phase diagram. These quantum phase transitions belong to the universality class of the commensurate-incommensurate phase transition. We also present a detailed numerical analysis of the low energy spectrum and the ground state magnetic phase diagram. In particular, we show that the intermediate state (h _c1 < h < h _c2) is gapful, describing the spin-flop phase.     

Domain structure in an ultrathin ferromagnetic film: Three-parameter model

A stripe domain structure (DS) was studied in an ultrathin ferromagnetic film under an in-plane magnetic field. The basic structure parameters (the amplitude and period of the DS, the thickness of domain walls) were determined within a unified variational approach, and transitions from the DS state to a homogeneous canted and a homogeneous planar phase were studied.     

Phase diagram of antiferromagnetic cobalt fluoride

The H-T phase diagram of antiferromagnetic cobalt fluoride in an external magnetic field H perpendicular to the easy magnetization axis A is completed and used to construct a phase diagram in the variables H _z and H _y . In this diagram, the lines corresponding to second-order phase transitions (between an angular phase and a phase with antiferromagnetic vector I ⊥ A) begin and end in fields of a spin-flip transition (i.e., in an exchange field). A peculiarity of these lines of phase transitions is that each of them has two tricritical points at which this line of second-order phase transitions transforms into a line of first-order phase transitions. A critical angle between the direction of the external magnetic field and the basal plane within which the first-order phase transition takes place is determined.     

Thermodynamic Properties of Random Transverse Field Mixed Spin System in the Presence of Single-Ion Anisotropy

We study the thermodynamic properties of random transverse field mixed spin system in the presence of single-ion anisotropy on a square lattice. By making use of the effective field theory and a cutting approximation, the detailed phase diagrams are described and some interesting results are found under trimodal random transverse field distribution. A small single-ion anisotropy can magnify magnetic ordering region at low temperatures and existence of a large transverse field can assist the occurrence of reentrant phenomena. With increasing disorder, second-order phase transitions are shown to change into first-order phase transitions. The trajectory of the tricritical point in the phase space as a function of disorder is presented. These indicate a strong correlation with the corresponding to trimodal transverse field distribution.     

Micro-transitions or breathers in L-alanine?

Within mean field approximation, a procedure is elaborated to consider noise induced phase transitions with arbitrary relations between the noises of different degrees of freedom. The proposed approach is applied to investigate effects of cross correlation between noises in the generalized synergetic model of Lorenz type. This cross correlation is shown to induce phase transitions of the dynamical system under consideration. Additionally, we find the correlation between noises transforms a synergetic behavior to a thermodynamic one. Received 13 November 2002 Published online 11 April 2003 RID="a" ID="a"e-mail: dikh@sumdu.edu.ua     

On accuracy of different cluster models used in describing ordering phase transitions in fcc alloys

A general formulation of cluster methods applied to calculations of thermodynamic quantities of alloys in terms of renormalizing fields describing interaction between a cluster and its environment is given. We have shown that the well-known cluster variation method and the cluster field method, which was suggested earlier, are special cases of our approach. These methods have been used in calculations of phase diagrams of fcc alloys with L1₂ and L1₀ ordering transitions with several realistic interaction models. It turns out that, for all these models, the simple tetrahedron version of the cluster field method suggested in this paper describes the phase diagrams almost as accurately as more complicated cluster variation techniques. Possible applications of the tetrahedron version of the cluster field method to inhomogeneous states and kinetics of phase transitions in fcc alloys are discussed. Zh. éksp. Teor. Fiz. 115, 158–179 (January 1999)     

Comparison of and comments on two thermodynamic approaches (reversible and irreversible) to ferroelectric phase transitions

In this article, we compared and commented on two thermodynamic approaches, i.e. the reversible and irreversible ones to ferroelectric phase transitions especially in the case of first-order. The reversible approach, otherwise known as the Landau–Devonshire theory proved not to possess a firm physical basis according to the concepts and methods originating from the field theory and those originating from the analytical dynamics. The metastable states hypothesis underlying the Landau–Devonshire theory causes an unpleasant consequence and a logical conflict. As for the new-developed irreversible approach, we demonstrated that the fundamental hypothesis of stationary states underlying it, is reliable with the aid of non-equilibrium variational principles. The difficulties encountered within the Landau–Devonshire theory can be overcome while this approach is applied to the first-order ferroelectric phase transitions. There is some justification made to prove the proposition.     

Spin-1/2 Ising model on a AFM/FM two-layer Bethe lattice in a staggered magnetic field

A bilayer spin-1/2 Ising model consisting of two superposed Bethe lattices with antiferromagnetic/ferromagnetic interactions is studied by the use of exact recursion relations in a pairwise approach in the presence of an external staggered magnetic field. Besides the ground state phase diagrams calculated in different possible planes of the model parameters space, the thermal variations of the order-parameters and the free energy are investigated to obtain the temperature-dependent phase diagrams of the model for different values of the coordination numbers q. Our calculations reveal that depending on the strength of the model parameters, the model exhibits a variety of interesting phase transitions and therefore phase diagrams.     

Signatures for “phase” transitions in finite systems

The existence of “phase” transitions in finite nuclear systems has been predicted in several models. However fluctuations in the relevant order parameters are generally large enough to prevent their use as signatures for the transitions. In present work both the specific heat and the square of the fluctuations in the internal energy over temperature squared have been calculated in a realistic calculation in²⁴Mg. These are equivalent in an exact canonical ensemble calculation for fixed particle number but differ in the thermal mean field approach. Both clearly indicate the presence of “phase” transitions, the first being more useful for the higher lying second order shape transitions, the second more appropriate for the lower lying first order transitions.     

Effect of an electric field on ferroelastic phase transitions

The effect of an external electric field on the proper ferroelastic phase transitions described in a two-dimensional representation of the D _4h class is analyzed theoretically. The electric field induces a Lifshitz invariant. It is shown that this invariant does not lead to the formation of an incommensurate phase. The phase diagram for commensurate transitions occurring under the action of an electric field changes significantly. The second-order phase transition from the initial phase is split by an electric field of specific orientation into a sequence of two second-order phase transitions with close temperatures.     

Smearing of phase transition due to a surface effect or a bulk inhomogeneity in ferroelectric nanostructures

The boundary conditions, customarily used in the Landau-type approach to ferroelectric thin films and nanostructures, have to be modified to take into account that a surface of a ferroelectric is a defect of a field type. The surface (interface) field is coupled to a normal component of polarization and, as a result, the second order phase transitions are generally suppressed and anomalies in response are washed out, as observed experimentally.     

An alternate version of Pirogov-Sinai theory

A new approach to the Pirogov-Sinai theory of phase transitions is developed, not employing the contour models with a parameter. The completeness of the phase diagram is proven.