Effect of elastic deformations on the critical behavior of disordered systems with long-range interactions

A field-theoretic approach is applied to describe behavior of three-dimensional, weakly disordered, elastically isotropic, compressible systems with long-range interactions at various values of a long-range interaction parameter. Renormalization-group equations are analyzed in the two-loop approximation by using the Padé-Borel summation technique. The fixed points corresponding to critical and tricritical behavior of the systems are determined. Elastic deformations are shown to changes in critical and tricritical behavior of disordered compressible systems with long-range interactions. The critical exponents characterizing a system in the critical and tricritical regions are determined.     

Experimental study of the electric-field-induced smectic A-ferroelectric smectic C critical point in binary mixtures: Approach to tricritical behavior

A system of binary mixtures of two liquid crystal compounds is prepared possessing a tricritical point in the smectic A-ferroelectric smectic C transition line in the temperature-composition plane. In several mixtures with different distinctness of the first-order nature of the transition the approximate coordinates of the electric-field-induced critical point, at which the first-order transition vanishes, are determined by measurements of the electric displacement. The critical field strength and the temperature difference between the transition at zero field and the critical point shrink to zero as the tricritical point is approached. This is the first study of the wing critical points of a tricritical point in liquid crystal phase transitions.     

Trimodal random-field spin- Ising systems in a transverse field

The trimodal random-field spin- Ising system in a transverse field is investigated by combining the pair approximation with the discretized path-integral representation by introducing a parameter p to simulate the fractions of the spins not exposed to the external longitudinal magnetic field. The variation of the critical reduced transverse field and longitudinal magnetic field with the parameter p is studied for different coordination numbers and it is found that the system does not exhibit any tricritical points for p>0.22. The phase diagrams with respect to the external longitudinal random-field and the second-order phase transition temperature are obtained for given values of the transverse field, coordination numbers and the parameter p. It is found that for appropriate values of the system parameters the system does present tricritical points and reentrant phase transitions, which may be caused by the competition between the quantum effects and randomness.     

Tricritical behavior of random systems with coupling to a nonfluctuating parameter

The influence of disordering upon the critical behavior of a system with hidden degrees of freedom is considered. It is shown that there is a tricritical behavior in the constrained system, while in the unconstrained system only phase transitions of the second order occur.     

The quantum transverse spin-2 Ising model with a bimodal random-field in the pair approximation

In this paper, we have investigated the bimodal random-field spin-2 Ising system in a transverse field by combining the pair approximation with the discretized path-integral representation. The exact equations for the second-order phase transition lines and tricritical points are obtained in terms of the random field H, the transverse field G and the coordination number z. It is found that there are some critical values for H and G where the tricritical points disappear for given z. We have also observed that the system presents reentrant behavior which may be caused by the quantum effects and randomness. The phase diagram with respect to the random field and the second-order phase transition temperature are studied extensively for given values of the transverse field and the coordination number.     

Magnetic fluids in an external field

Within mean field approximation we investigate the phase diagrams of magnetic fluids in presence of a magnetic field. In a finite field the magnetic phase transition is absent, but instead a line of first order liquid-liquid transitions ending in a critical point occurs for a magnetic interaction, which is sufficiently strong. Varying the magnetic field these critical points extend from the tricritical point at H=0 to a critical endpoint. For a fluid with Ising spins we calculate the critical lines and several tricritical exponents analytically. For Heisenberg fluids we obtain the phase diagrams from a numerical solution of the mean field equations of state. Received 20 March 1998     

Phase transitions and multicritical points in the mixed spin-3/2 and spin-2 Ising model with different single-ion anisotropies

The phase diagram of mixed spin-3/2 and spin-2 Ising ferromagnetic model with different single-ion anisotropies is investigated by the use of a mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. Global phase diagrams are obtained in the temperature-anisotropy plane. In particular, by changing values of the single-ion anisotropies, several different types of phase diagrams of first-order transition between two ordered phases, are studied in detail. A variety of multicritical points such as tricritical points, isolated critical points, and triple points are obtained.     

Nonclassical equations of state for critical and tricritical points

We develop a method by which certain classical equations of state may be modified to produce nonclassical critical scaling behavior. We then apply this method to the classical free energy describing a tricritical point that was originally introduced by Griffiths. The phase behavior of the resulting nonclassical free energy is characterized by the competition between critical scaling and tricritical scaling already envisioned by previous authors.Work supported by the National Science Foundation and the Cornell University Materials Science Center.Footnotes 3–10 of Ref. 1 provide a comprehensive list of experimental investigations of tricritical points in fluid mixtures.     

Multicritical dynamical phase diagrams of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling in an oscillating field

We study, within a mean-field approach, the stationary states of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling under the presence of a time-varying (sinusoidal) magnetic field. We employ the Glauber-type stochastic dynamics to construct set of dynamic equations of motion. The behavior of the time dependence of the order parameters and the behavior of the average order parameters in a period, which is also called the dynamic order parameters, as functions of the reduced temperature are investigated. The dynamic phase transition points are calculated and phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. The dynamical transition from one regime to the other can be of first- or second order depending on the region in the phase diagram. According to the values of the crystal field interaction or single-ion anisotropy constant and biquadratic exchange constant, we find 20 fundamental types of phase diagrams which exhibit many dynamic critical points, such as tricritical points, zero-temperature critical points, double critical end points, critical end point, triple point and multicritical point. Moreover, besides a disordered and ordered phases, seven coexistence phase regions exist in the system.     

Phase diagram and phase transitions of the adsorbate system S/Ru(0001): a Monte Carlo study of a lattice gas model

We investigate the phase diagram and the critical properties of the adsorbate system sulphur/ruthenium(0001) in the coverage region 0 < Θ < 1/3 using Monte Carlo simulations of a lattice gas model on a triangular lattice. From experiments it is known that for low coverages an island phase appears in the phase diagram of this system at low temperatures. To capture this feature we include in our lattice gas model a weak third neighbour attraction in addition to the repulsive first and second neighbour forces. The phase diagram obtained from simulations of this model is in very good agreement with the experimental phase diagram. The critical properties of the lattice gas model are found to be compatible with the results of experiments on the system sulphur/ruthenium(0001). Finer details of the phase diagram, e. g. the location of tricritical points, which may be difficult to assess experimentally will also be discussed.     

Multicritical behavior in ferroelectrics

Solid state systems exhibit besides usual second order phase transitions a rich variety of multicritical phenomena like Lifshitz points (or lines), tricritical points (or lines) and even tricritical Lifshitz points. Realizations of such points are numerous and were also verified in the family of ferroelectrics of the type (Pb_ySn_1y)₂P₂(Se_xS_1-x)₆. A review of the critical behavior at such points is presented here. Because of the importance of the uniaxial dipolar interaction in ferroelectrics the critical behavior is different from systems with short range interaction only. Moreover the coupling to the elastic degrees of freedom may not be neglected, and leads under certain conditions to a critical temperature dependence in certain elastic constants. Crossover phenomena, which are expected in the experimental accessible region of experiments are also considered.     

Dynamic phase transition in the kinetic spin-1 Blume-Capel model: Phase diagrams in the temperature and crystal-field interaction plane

Within a mean-field approach, the stationary states of the kinetic spin-1 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field is studied. The Glauber-type stochastic dynamics is used to describe the time evolution of the system and obtain the mean-field dynamic equation of motion. The dynamic phase-transition points are calculated and phase diagrams are presented in the temperature and crystal-field interaction plane. According to the values of the magnetic field amplitude, three fundamental types of phase diagrams are found: One exhibits a dynamic tricritical point, while the other two exhibit a dynamic zero-temperature critical point. The text was submitted by the authors in English.     

Pressure-induced tricritical point and critical behavior near the points of phase-diagram wings in a CoS<Subscript>2</Subscript> ferromagnet

A pressure-induced change in the order of magnetic phase transition observed for CoS₂ in [1] is explained using the exchange-striction ferromagnet model allowing for the first-and second-order magnetoelastic interactions. It is shown that this model offers a satisfactory quantitative explanation of the majority of experimental facts observed in CoS₂. The magnetic phase diagram of CoS₂ is calculated in the vicinity of a tricritical point in the temperature (T), pressure (P), and magnetic-field (H) variables. The critical behavior of the thermodynamic quantities near the tricritical points of phase-diagram wings is discussed.     

无规场非晶化表面的临界行为

应用平均场重整化群方法,讨论表面无规场和非晶化存在对S=1和σ=1/2混合自旋伊辛系统表面磁性临界行为的影响,得到在各种情况下系统的表面相图.计算结果表明,非晶化在一定范围内与无规场竞争仍可出现三临界点和重入现象. 关键词：     

A discussion of critical behaviour in a mixed-spin Ising model

The critical behaviour of a mixed and spin-1 Ising system is investigated by the use of the two-site cluster effective-field theory. The general expressions for evaluating the transition temperature and the tricritical point are obtained. Particular attention is drawn to the tricritical behaviour of the square lattice and it is shown that it strongly depends on the accuracy of calculations with a tendency to disappear when the accuracy is improved.     

Thermodynamic properties of ferromagnets with uniaxial and biaxial anisotropy

The thermodynamic properties of spin-one Heisenberg ferromagnets with uniaxial and biaxial anisotropy are investigated in the molecular field approximation (MFA) and random phase approximation (RPA). In MFA a full phase diagram comprising three lines of bicritical points, is obtained.Using the standard-basis operator method, the collective excitation spectrum is studied in detail; moreover the softening of the excitations at the phase boundaries is discussed. A self-consistent version of RPA with emphasis on the role of kinematic restrictions with regard to the standard-basis operators is analyzed.Moreover, the phase transitions are considered in the Ising model, where a line of tricritical points occurs, and the planar model, where a line of bicritical points, two lines of tricritical points and a line of triple points, occur.     

The Glauber dynamics for a spin-1 metamagnetic Ising system with bilinear and biquadratic interactions

We present a study, within a mean-field approximation, of the dynamics of a spin-1 metamagnetic Ising system with bilinear and biquadratic interactions in the presence of a time-dependent oscillating external magnetic field. First, we employ the Glauber transition rates to construct the set of mean-field dynamic equations. Then, we study the time variation of the average order parameters to find the phases in the system. We also investigate the thermal behavior of dynamic order parameters to characterize the nature (first- or second-order) of the dynamic transitions. The dynamic phase transitions are obtained and the phase diagrams are constructed in two different the planes. The phase diagrams contain a disordered and ordered phases, and four different mixed phases that strongly depend on interaction parameters. Phase diagrams also display one or two dynamic tricritical points, a dynamic double critical end and dynamic quadruple points. A comparison is made with the results of the other metamagnetic Ising systems.     

The phase-transition order parameter, fluctuations, and nanoclusters in benzil crystals

Bragg and diffuse X-ray reflections from the M points of the Brillouin zone boundary of a benzil crystal paraphrase, the integral intensity of which is associated with the order parameter and its fluctuations, are studied. Original data on the temperature behavior of the order parameter and diffuse scattering are obtained. The relevant critical exponents are determined. A conclusion is drawn as to the proximity of the phase transition in these crystals to the tricritical point. A phase transition model is discussed.