Tricritical point in classical spin systems with random transverse fields

The existence of a tricritical point is demonstrated for a classical n-vector model with annealed random transverse fields, and the corresponding tricritical temperature T_t and distribution width σ_t are evaluated within Landau theory for continuous spin dimensionality -2 < n < 10.     

An exactly soluble model with tricritical points for structural-phase transitions

We present and study a lattice-dynamical model whose static and dynamic properties can be described exactly for all dimensionsd≧3 (d an integer) and which, in addition, exhibits tricritical points. For certain model parameters, the tricritical behaviour is found to be identical to that of the spherical model. By changing the model parameters continuously however, the transition suddenly becomes of first order at a tricritical point (TCP). The order parameter and the susceptibility are given explicitly ford≧3. The tricritical exponents are Gaussian. The critical dynamics is also discussed.     

On the tricritical point induced by random transverse fields

In contradiction to a paper of Pirc it is shown that for a classical n-vector model with annealed random transverse fields only the second-order phase transition is possible and no tricritical points appear. The free energy functional for such systems is evaluated within the Landau theory.     

Second-phase nucleation on an edge dislocation

A model for nucleation of second phase at or around a dislocation in a crystalline solid is considered. The model employs the Ginzburg–Landau theory of phase transitions comprising the sextic term in the order parameter (η⁶) in the Landau free energy. The ground state solution of the linearised time-independent Ginzburg–Landau equation is derived, through which the spatial variation of the order parameter is delineated. Moreover, a generic phase diagram indicating tricritical behaviour near and away from the dislocation is depicted. The relation between classical nucleation theory and the Ginzburg–Landau approach is discussed, for which the critical formation energy of the nucleus is related to the maximum of the Landau potential energy. A numerical example illustrating the application of the model to the case of nucleation of hydrides in zirconium alloys is provided.     

Tricritical phase transitions in semi-infinite systems

Semi-infinite systems with a bulk tricritical point are studied using a free energy functional of the Ginzburg-Landau-Wilson type. Tricritical surface exponents, order parameter profiles and the phase diagram are presented within mean field theory. In the case of ordinary and special transition, renormalization-group methods are used to obtain the exponents of a system withO(n)-symmetry to first order in ?=3?d and logarithmic corrections ind=3.     

Behavior of the antiferromagnetic phase transition near the fermion condensation quantum phase transition in YbRh2Si2

Low-temperature specific-heat measurements on YbRh₂Si₂ at the second order antiferromagnetic (AF) phase transition reveal a sharp peak at TN=72 mK. The corresponding critical exponent α turns out to be α=0.38, which differs significantly from that obtained within the framework of the fluctuation theory of second order phase transitions based on the scale invariance, where α?0.1. We show that under the application of magnetic field the curve of the second order AF phase transitions passes into a curve of the first order ones at the tricritical point leading to a violation of the critical universality of the fluctuation theory. This change of the phase transition is generated by the fermion condensation quantum phase transition. Near the tricritical point the Landau theory of second order phase transitions is applicable and gives α?1/2. We demonstrate that this value of α is in good agreement with the specific-heat measurements.     

Scaling laws connecting tricritical and normal critical exponents for dimensionsd≦3

The method of Imry, Deutscher, Bergman and Alexander for deriving interdimensional scaling laws is used in a modified form to establish scaling relations between tricritical and normal critical exponents. These relations are expected to hold for dimensionsd≦ 3. The tricritical behaviour ford=3 andd>3 has previously been discussed by Wegner and Riedel and by the author.     

Landau behaviour of the heat capacity of AgNa(NO2)2 close to the nearly tricritical ferroelectric phase transition

The heat capacity of a single crystal of the uniaxial ferroelectric AgNa(NO₂)₂ was measured close to the nearly tricritical phase transition. In the ferroelectric phase a strong temperature dependence of the anomaleous specific heat is found which obeys a temperature law (θ _f —T)^?0.494. A small latent heat was detected nearT _c. The thermal behaviour of AgNa(NO₂)₂ is described by a Landau type theory, from which the non linear coefficientsζ andζ of the free energy expansion are derived. The thermal data fit well to the known dielectric behaviour.     

On the specific heat of Fermi liquids

The contributions of long-wavelength spin fluctuations to the specific heat of Fermi liquids is consistently calculated on the basis of the Landau theory of Fermi liquids. More satisfactory estimations of the Landau parameter F₁^a for liquid ³He are obtained.     

Effect of γ irradiation on the heat capacity of (CH3)2NH2Al(SO4)2 · 6H2O crystals near the ferroelectric phase transition

The heat capacity of dimethyl ammonium-aluminum sulfate crystals (DMAAS), both nonirradiated and γ-irradiated to fluences of 10⁷, 5×10⁷, and 10⁸ R, has been measured by the adiabatic method near the ferroelectric phase transition (PT) within the 80–300 K temperature range. The C _p =f(T) curve exhibits a λ-shaped anomaly near the phase-transition point T _C =152 K. The PT temperature and the magnitude of the anomaly are shown to decrease with increasing γ-irradiation fluence. It has been established that the ferroelectric PT at T _C =152 K, which lies close to the tricritical point, shifts progressively more under γ irradiation toward the second-order PT, and that the behavior of the anomalous part of the heat capacity in the ferroelectric phase is described by the thermodynamic theory of Landau. The experimental heat-capacity data have been used to calculate the variation of the thermodynamic functions of the DMAAS crystal.     

Dielectric studies of phase transitions in the ferroelectric CdTiO3 and the Sr1−x CdxTiO3 solid solution

Temperature dependences of the permittivity and of the dielectric hysteresis loops in ceramic samples of nominally pure CdTiO₃ and a Sr_1?x Cd_xTiO₃ solid solution were studied. At 76.5±0.5 K, CdTiO₃ was established to undergo a ferroelectric phase transition close to the tricritical point. The temperature dependence of spontaneous polarization of CdTiO₃ is described within the Landau theory of phase transitions with the critical order parameter exponent ≈0.25. The phase diagram of the Sr_1?x Cd_xTiO₃ solid solution was drawn in (T, x) coordinates, and the critical concentration x _c =0.002, above which an induced polar state sets in the solid solution, was determined.     

Lie-Poincaré transformations and a reduction criterion in Landau theory

In the Landau theory of phase transitions one considers an effective potential Φ whose symmetry group G and degree d depend on the system under consideration; generally speaking, Φ is the most general G-invariant polynomial of degree d. When such a Φ turns out to be too complicate for a direct analysis, it is essential to be able to drop unessential terms, i.e., to apply a simplifying criterion. Criteria based on singularity theory exist and have a rigorous foundation, but are often very difficult to apply in practice. Here we consider a simplifying criterion (as stated by Gufan) and rigorously justify it on the basis of classical Lie-Poincaré theory as far as one deals with fixed values of the control parameter(s) in the Landau potential; when one considers a range of values, in particular near a phase transition, the criterion has to be accordingly partially modified, as we discuss. We consider some specific cases of group G as examples, and study in detail the application to the Sergienko-Gufan-Urazhdin model for highly piezoelectric perovskites.     

Specific heat and latent heat of KMnF3 ferroelastic crystal

The specific heat and the heat flux exchanged by a single crystal of KMnF₃ have been measured simultaneously while cooling the sample at constant rate of 0·06 K/h through the phase transition at T ₀= 186 K. The phase transition is weakly first order and close to a tricritical point. The temperature dependence at T185 K of the excess specific heat and the excess entropy follow very well the predictions of a Landau potential at a tricritical point.     

On a microscopic theory of liquid 3He

We present a microscopic calculation of the wave number dependent quasiparticle interaction and its variation with pressure in liquid ³He. Calculation of the variation of the Landau parameters F^s₀ and F^a₀ with pressure is also presented. The theory is capable of reproducing qualitatively some of the salient features seen in experiments in liquid ³He.     

Effects of the phase transition in Hg2(Br,I)2 crystals

The effects of the phase transition in Hg₂(Br,I)₂ crystals have been investigated over a wide range of temperatures by the Raman scattering spectroscopy and X-ray diffraction analysis. The overtones (at the X point of the Brillouin zone boundary) and the fundamental tones (at the center of Brillouin zone) of soft modes are found in the Raman spectra of these crystals and studied in detail. The density of one-phonon states of the soft TA branch manifests itself in the Raman spectra of mixed crystals. The potentialities of the soft-mode spectroscopy are realized in full measure. Analysis of the ratio between intensities of overtones and fundamental tones of the soft modes has demonstrated the applicability of the Landau phenomenological theory of phase transitions. The orthorhombic splitting of the reflections corresponding to the basal plane is revealed in the X-ray diffraction patterns and thoroughly explored. The temperature dependences of the isotropic and shear spontaneous strains are obtained. It is shown that the shear spontaneous strain plays a decisive role. The critical indices are determined and the model of the improper ferroelastic phase transition D _4h ¹⁷ → D _2h ¹⁷ in the vicinity of the tricritical point is corroborated.     

The pressure effect on the CDW-transition temperatures in 1T-TaS2

The pressure dependence of the two CDW transition temperatures (T_d1? 350 K and T_d2 ～ 190 K) in 1T-TaS₂ has been investigated by measuring the resistivity up to 5 kbar. It is found that the thermal hysteresis of the phase transition at T_d2 is very sensitive to the pressure and is interpreted by the phenomenological Landau theory including cubic term.     

Excitation functions for the production of90Nb and88Y by irradiation of zirconium with deuterons

Excitation functions for reactions induced by deuterons on natural zirconium and⁹⁰Zr targets have been measured radiochemically with the stacked foil technique between ≈9 and 27 MeV. The observed reactions are Zr(d,xn)⁹⁰ Nb, Zr(d,axn)⁸⁸Y,⁹⁰Zr(d, 2n)⁹⁰Nb and⁹⁰Zr(d, α)⁸⁸Y. The excitation functions for the reactions⁹¹Zr(d, 3n)⁹⁰Nb and⁹¹Zr(d, αn)⁸⁸Y have been deduced from the results mentioned above. Calculations of the excitation function for the (d, 2n) reaction have been performed with two different treatments, each one taking into account two competitive mechanisms. The compound-statistical model plus Hittmair's stripping theory accounts quite well for the (d, 2n) cross sections observed. However, the agreement obtained with Peaslee-Otozai's theory is excellent and the set of parameters used more reasonable. It has been assumed that the stripping mechanism can have no contribution to the (d, α) reaction. Accordingly, calculations for this reaction have been done using the compound-statistical model and the entire absorption process followed by the evaporation of an α particle. No good agreement is obtained with either theory.     

Classical Heisenberg ferromagnets with defects

A ferromagnet (dimensionality d) containing defects (of dimensionality d′) is treated by the phenomenological Landau theory. It is shown that for d′<d?1 no change of the critical exponent of the local magnetization near the defect occurs, in contrast to the case of the local magnetization near a surface (d′=d?1). The case of point defects (d′=0) in classical Heisenberg ferromagnets with nearest neighbor interactions is treated both by the mean field approximation and the Monte-Carlo method with effective field boundary conditions. We obtain rough agreement between these two approaches—two special cases are considered in detail: (a) interaction with, the defect being zero, (b) anti-ferromagnetic interactions across the defect (which is a crude model of superexchange). It is pointed out that it is a reasonable approximation to express the deviation of the local magnetization from the bulk value near the defect in terms of the spin pair correlation functions of the undisturbed system.