Tricritical Behavior Research Articles

Determination of the orientational order parameter of the homologous series of 4-cyanophenyl 4-alkylbenzoate (n.CN) by different methods

The orientational order parameters of a homologous series of 4-cyanophenyl 4-alkylbenzoates have been determined at different temperatures from 13C-NMR, x-ray diffraction, optical birefringence, high resolution density and diamagnetic susceptibility anisotropy measurements. To determine the temperature dependence of the orientational order parameter from the 13C chemical shift values, the two-dimensional polarization inversion spin exchange at the magic angle (PISEMA) method was also used for the measurement of 13C–1H dipolar couplings at different sites in the oriented phase. The nematic order parameters determined from each of these methods have been compared. Apart from a slight shift in their values their trends with temperature are very similar. The differences among the results obtained by these five different methods have been discussed. From the high resolution density data, the values of the critical exponents near the TN−I transition are found to lie between the Ising model and tricritical behaviour.

Optical Transmission Factor of a Ferronematic Liquid Crystal Under Magnetic Field Induced Orientational Transitions

In the framework of continuum theory we study the light transmission factor of a ferronematic liquid crystal as a function of external magnetic field, the anchoring energy with the boundary of a layer, and material parameters of a ferronematic. We show that magnetic field induced Fréedericksz transition in ferronematics in twist geometry can be either a first- or second-order phase transition depending on the anchoring energy between the director and magnetic particles, i.e., it exhibits the tricritical behavior. The light transmission factor for first- or second-order transition is also studied.

Reentrant Phase Transitions in Ferronematic Liquid Crystals

Within the continuum theory we study the influence of codirectional electric and magnetic fields on the orientational structure of a ferronematic layer taking into account the segregation effects. Recently in [Phys. Rev. E 81, 051710 (2010)] the tricritical behavior of the magnetic Freedericksz transition in ferronematics has been theoretically predicted. This paper shows that an external electric field can change the character of this transition. We find reentrant Freedericksz transitions in ferronematic liquid crystals subjected to the electric and magnetic fields. These transitions can be either first- or second-order ones. We derive the analytical expression for the width of the area of the reentrant orientational transitions.

Noneqilibrium Phase Transition in Kinetic Ising Model: Absence of Tricritical behaviour in Presence of Impurities

The nonequilibrium dynamic phase transition, in the two dimensional site diluted kinetic Ising model in presence of an oscillating magnetic field, has been studied by Monte Carlo simulation. The projections of dynamical phase surface are drawn in the planes formed by the dilution and field amplitude and the plane formed by temperature and field amplitude. The tricritical behaviour is found to be absent in this case which was observed in the pure system.

Interplay between dipole and quadrupole modes of field influence in liquid-crystalline suspensions of ferromagnetic particles

In the framework of continuum theory we study orientational transitions induced by electric and magnetic fields in ferronematics, i.e., in liquid-crystalline suspensions of ferromagnetic particles. We have shown that in a certain electric field range the magnetic field can induce a sequence of re-entrant orientational transitions in ferronematic layer: nonuniform phase --- uniform phase --- nonuniform phase. This phenomenon is caused by the interplay between the dipole (ferromagnetic) and quadrupole (dielectric and diamagnetic) mechanisms of the field influence on a ferronematic structure. We have found that these re-entrant Freedericksz transitions exhibit tricritical behavior, i.e., they can be of the first or the second order. The character of the transitions depends on a degree of redistribution of magnetic admixture in the sample exposed to uniform magnetic field (magnetic segregation). We demonstrate how electric and magnetic fields can change the order of orientational transitions in ferronematics. We show that electric Freedericksz transitions in ferronematics subjected to magnetic field have no re-entrant nature. Tricritical segregation parameters for the transitions induced by electric or magnetic fields are obtained analytically. We demonstrate the re-entrant behavior of ferronematic by numerical simulations of the magnetization and optical phase lag.

Discontinuous percolation transitions in real physical systems

We study discontinuous percolation transitions (PTs) in the diffusion-limited cluster aggregation model of the sol-gel transition as an example of real physical systems, in which the number of aggregation events is regarded as the number of bonds occupied in the system. When particles are Brownian, in which cluster velocity depends on cluster size as v(s)~s(η) with η=-0.5, a larger cluster has less probability to collide with other clusters because of its smaller mobility. Thus, the cluster is effectively more suppressed in growth of its size. Then the giant cluster size increases drastically by merging those suppressed clusters near the percolation threshold, exhibiting a discontinuous PT. We also study the tricritical behavior by controlling the parameter η, and the tricritical point is determined by introducing an asymmetric Smoluchowski equation.

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 behavior of the R I–R V rotator phase transition in a mixture of alkanes with nanoparticles

A phenomenological theory is presented, which describes the tricritical behavior of the R(I)-R(V) rotator phase transition in the mixture of alkanes with nanoparticles. The influence of the nanoparticles on the R(I)-R(V) transition in alkanes is discussed by varying the coupling between the order parameters of the rotator phases and nanoparticle. When nanoparticle solutes are added to pure alkanes, the R(I)-R(V) transition temperature is increased. It was observed from the theoretical calculations that for a particular value of the concentration of the nanoparticles, the first order R(I)-R(V) transition becomes second order at a tricritical point. Calculations based on this model agree qualitatively with experiment.

Mixed spin Ising model with four-spin interaction and random crystal field

The effects of fluctuations of the crystal field on the phase diagram of the mixed spin-1/2 and spin-1 Ising model with four-spin interactions are investigated within the finite cluster approximation based on a single-site cluster theory. The state equations are derived for the two-dimensional square lattice. It has been found that the system exhibits a variety of interesting features resulting from the fluctuation of the crystal field interactions. In particular, for low mean value D of the crystal field, the critical temperature is not very sensitive to fluctuations and all transitions are of second order for any value of the four-spin interactions. But for relatively high D, the transition temperature depends on the fluctuation of the crystal field, and the system undergoes tricritical behaviour for any strength of the four-spin interactions. We have also found that the model may exhibit reentrance for appropriate values of the system parameters.

Dynamic phase transitions and dynamic phase diagrams of the spin-2 Blume–Capel model under an oscillating magnetic field within the effective-field theory

The dynamic phase transitions are studied in the kinetic spin-2 Blume–Capel model under a time-dependent oscillating magnetic field using the effective-field theory with correlations. The effective-field dynamic equation for the average magnetization is derived by employing the Glauber transition rates and the phases in the system are obtained by solving this dynamic equation. The nature (first- or second-order) of the dynamic phase transition is characterized by investigating the thermal behavior of the dynamic magnetization and the dynamic phase transition temperatures are obtained. The dynamic phase diagrams are constructed in the reduced temperature and magnetic field amplitude plane and are of seven fundamental types. Phase diagrams contain the paramagnetic (P), ferromagnetic-2 (F2) and three coexistence or mixed phase regions, namely the F2+P, F1+P and F2+F1+P, which strongly depend on the crystal-field interaction (D) parameter. The system also exhibits the dynamic tricritical behavior.

Ultrasoft primitive model of polyionic solutions: Structure, aggregation, and dynamics

We introduce an ultrasoft core model of interpenetrating polycations and polyanions, with continuous Gaussian charge distributions, to investigate polyelectrolyte aggregation in dilute and semi-dilute salt-free solutions. The model is studied by a combination of approximate theories (random phase approximation and hypernetted chain theory) and numerical simulations. The calculated pair structure, thermodynamics, phase diagram, and polyion dynamics of the symmetric version of the model (the "ultrasoft restricted primitive model" or UPRM) differ from the corresponding properties of the widely studied "restricted primitive model" (RPM) where ions have hard cores. At sufficiently low temperatures and densities, oppositely charged polyions form weakly interacting, polarizable neutral pairs. The clustering probabilities, dielectric behavior, and electrical conductivity point to a line of sharp conductor-insulator transitions in the density-temperature plane. At very low temperatures, the conductor-insulator transition line terminates near the top of a first order coexistence curve separating a high-density liquid phase from a low-density vapor phase. The simulation data hint at a tricritical behavior, reminiscent of that observed for the two-dimensional Coulomb gas, which contrasts with the Ising criticality of its three-dimensional counterpart, the RPM.

The measurements of coexistence curves and critical behavior of a binary mixture with a high molecular weight polymer

The critical behavior of solutions of poly (diallydimethylammonium chloride) (PDDAC, M w = 3.2 × 10 5) in the critical binary mixture of isobutyric acid (I) + water (W) was studied by the refractive index measurements. The measurements were performed at three different PDDAC concentrations near and far away from the critical point. We observed that the critical temperatures increase linearly with increasing the concentration of PDDAC. As the distance from the critical point increases, the system exhibits a crossover from the renormalized Ising critical behavior to the mean-field one. For the solutions with the highest PDDAC concentration, experiments suggest a crossover to tricritical behavior.

Direct Observation of Diffuse Cone Behavior in de Vries Smectic-Aand -CPhases of Organosiloxane Mesogens

Simultaneous and direct x-ray measurements of the smectic layer spacing, molecular tilt, and orientational order in the de Vries smectic A (SmA) and C (SmC) phases of two organosiloxane mesogens reveal that (i) the SmC (tilt) order parameter exponent β=0.26±0.01 for 2nd order SmA-SmC transition--in excellent agreement with the tricritical behavior, (ii) the siloxane and hydrocarbon parts of the molecules are segregated and oriented parallel to the director with very different degree of orientational order, and (iii) thermal evolution of the effective molecular length is different in the two phases.

Regions of different critical behavior of the two-flavor Nambu–Jona-Lasinio model

We study the chiral phase diagram in the $T$-$\ensuremath{\mu}$-${m}_{0}$ space of the two-flavor Nambu-Jona-Lasinio model with the approach of the Landau theory of phase transitions. The tricritical point (TCP) is an endpoint of a line of triple points as well as a crosspoint of three $\ensuremath{\lambda}$-transition lines. These double characters bring the connective and consistent problem of a critical phenomenon at the TCP. There is a crossover region from normal critical to tricritical behavior near the TCP, no matter whether the current quark mass is zero or not. The critical exponents need to be renormalized when one approaches the TCP along the first-order phase-transition line.

Laboratory parallel-beam transmission X-ray powder diffraction investigation of the thermal behavior of calcite: comparison with X-ray single-crystal and synchrotron powder diffraction data

Periodico di Mineralogia (2011), 80, 1 (Special Issue), 123-134 - DOI: 10.2451/2011PM0010 Special Issue in memory of Sergio Lucchesi Laboratory parallel-beam transmission X-ray powder diffraction investigation of the thermal behavior of calcite: comparison with X-ray single-crystal and synchrotron powder diffraction data Paolo Ballirano Dipartimento di Scienze della Terra, Sapienza Universita degli Studi di Roma, Italy paolo.ballirano@uniroma1.it Abstract Thermal behavior of calcite has been analyzed in the 303-1098 K thermal range by laboratory parallel-beam transmission X-ray powder diffraction. Present results provide a clear indication of the possibility to extract high-quality structural data from such instrumental set up. Such quality has been proved to be at the same level of a mid eighties X-ray single crystal investigation. Analysis of the spontaneous strain e 33 provides a critical exponent Β of 0.2499(5) consistent with the value of ¼ expected for a tricritical behavior. Structure refinements seemengly support the Ising model of disorder. Key words : high-temperature X-ray powder diffraction; Rietveld method; calcite; nitratine; order/disorder phase transition; spontaneous strain.

Mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice within the effective-field theory

An effective-field theory with correlations is developed for a mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice. Spin-1 atoms and spin-3/2 atoms are distributed in alternative layers of a honeycomb lattice. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the interaction between the vertically aligned spins and adjacent spins are coupled either ferromagnetically or antiferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the temperature dependence of the total magnetization to find the compensation points and to determine the type of compensation behavior. We present the phase diagrams in different planes for h = 0 , and the phase diagrams contain the paramagnetic, nonmagnetic and ferrimagnetic phases. The system also presents a tricritical behavior besides multicritical point ( A ) , isolated critical point ( C ) and double critical end point ( B ) depending on the interaction parameters.

Monte Carlo study of the two-dimensional vector Blume-Capel model

The Blume-Capel model (BCM) generalizes the Ising model to allow for the presence of vacancy sites, and was used as an early description of the effect of a $^{3}\text{H}\text{e}$ admixture on the $^{4}\text{H}\text{e}$ superfluid transition, especially tricritical behavior. The vector counterpart of the BCM improves upon the original by utilizing spins with a continuous symmetry, the correct universality class for superfluidity. This paper presents a Monte Carlo calculation of the full phase diagram of the two-dimensional vector BCM. A tricritical point is shown to separate a first-order phase transition line at low temperature from a Kosterlitz-Thouless boundary at higher temperature and the location of the tricritical point is determined.

Thermal expansion of the Sn2P2(Se0.28S0.72)6 solid solutions

In the present work, we have experimentally studied and analysed the dilatometric properties of Sn2P2(Se0.28S0.72)6 crystals during ferroelectric phase transition. A complete matrix of thermal expansion tensors as well as the characteristic surface of the thermal expansion tensor has been obtained. The critical exponent for the volume thermal expansion coefficient in Sn2P2(Se0.28S0.72)6 crystals has been determined to be equal to 0.50 ± 0.06, which is peculiar to tricritical behaviour. Non-agreement in the values of the critical exponents evaluated from the temperature dependencies of relative elongation (0.17 ± 0.01) and volume thermal expansion coefficient (0.50 ± 0.06) is shown to be due to the possible temperature rotation of the spontaneous polarisation vector.

On the relation between Vicsek and Kuramoto models of spontaneous synchronization

The Vicsek model for self-propelling particles in 2D is investigated with respect to the addition of the stochastic perturbation of dynamic equations. We show that this model represents in essence the same type of bifurcations under a different type of noise as the celebrated Kuramoto model of spontaneous synchronization. These models demonstrate similar behavior at least within the mean-field approach. To prove this we consider two types of noise for the Vicsek model which are commonly considered in the literature: the intrinsic and the extrinsic ones (according to the terminology of Pimentel et al. [J.A. Pimentel, M. Aldana, C. Huepe, H. Larralde, Intrinsic and extrinsic noise effects on phase transitions of network models with applications to swarming systems, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (6) (2008) doi:10.1103/PhysRevE.77.061138. URL: http://dx.doi.org/10.1103/PhysRevE.77.061138]). The qualitative correspondence with the bifurcation of stationary states in the Kuramoto model is stated. A new type of stochastic perturbation—the “mixed” noise is proposed. It is constructed as the weighted superposition of the intrinsic and the extrinsic noises. The corresponding phase diagram “noise amplitude vs. interaction strength” is obtained. The possibility of the tricritical behavior for the Vicsek model is predicted.

Tricritical Behavior of Sn2P2S6 Ferroelectrics at Hydrostatic Pressure

For Sn2P2S6 ferroelectrics with three-well potential under hydrostatic compression the second order phase transition approaches tricritical point as expected according to Blume-Emery-Griffiths (BEG) model. Joint consideration of BEG model and known ANNNI model, describing the incommensurate phase appearing as a result of competitive interactions, allows one to draw conclusion about possibility of tricritical point presence on temperature-pressure diagram of Sn2P2S6 without incommensurate phase appearing. Investigations of temperature dependences of longitudinal ultrasound velocity at different pressures for Sn2P2S6 crystals confirm such conclusion.