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.     

Effects of point defects on the phase diagram of vortex states in high- T(c) superconductors in the B parallel to c axis

The phase diagram for the vortex states of high- T(c) superconductors with point defects in the B--> parallel to c axis is drawn by large-scale Monte Carlo simulations. The vortex slush (VS) phase is found between the vortex glass (VG) and vortex liquid (VL) phases. The first-order transition between this novel normal phase and the VL phase is characterized by a sharp jump of the density of dislocations. The first-order transition between the Bragg glass (BG) and VG or VS phases is also clarified. These two transitions are compared with the melting transition between the BG and VL phases.     

Landau theory of shape phase transitions in the cranked interacting boson model

Landau theory of phase transitions is applied to quadrupole shapes of rotating atomic nuclei within the interacting boson model (IBM) with cranking. It is shown that the coherent-state method must be generalized to allow for non-Hermitian quadrupole tensors of the coherent-state coefficients, which results in important modifications of the cranking shape-phase diagram compared to previous non-IBM studies of rotating nuclei. The parameter space has two surfaces of the first-order phase transitions and a curve of the second-order phase transition at their intersection. The phase structure of the cranked IBM closely resembles systems with competing superconducting and normal phases.     

First and second order phase transitions in gauge theories at finite temperature

We consider in general the nature of the phase transition which occurs in 4D gauge theories coupled to scalar and spinor fields at finite temperature. It is shown that the critical behavior can be isolated in an effective 3D theory of the zero frequency mode whose lagrangian may be calculated explicitly in weak coupling perturbation theory. This lagrangian, in turn, may be investigated by means of standard ?-expansion techniques. Theories with an asymptotically free gauge coupling constant possess no stable fixed point in the ?-expansion and are inferred to have weakly first-order phase transitions; theories not satisfying this condition may have second-order transitions.     

The role of elastic strains at non-ferroelastic displacive phase transitions

The role of elastic strains at structural phase transitions is illustrated within the Landau theory and its first-order corrections due to critical fluctuations and defects are described. The Landau theory is sufficient to demonstrate the impossibility of bulk nucleation in a supercooled symmetrical phase and the absence of heterophase fluctuations in solids. The critical fluctuations are known to convert a second-order transition in an Ising-like system in a solid to a first-order one. Close to the mean-field tricritical point the effect can be described, for displacive systems, within a first-order perturbation theory and takes place for the Heisenberg systems as well. The influence of defects on these transitions is mediated essentially by the elastic strains. Defects smear the transition. For the “random local field” defects and an incommensurate (Heisenberg-like) transition this effect is so strong that first-order perturbation theory leads to a divergence.     

Behavior of the p-T phase diagram of the organic conductor (ET)4Hg3I8

The conductivity of single crystals of the organic conductor (ET)₄Hg₃I₈ [ET-bis(ethylendithio)tetrathiafulvalene] has been investigated at temperatures from 4.2 to 360 K and pressures of up to 75 kbar. Two first-order phase transitions have been detected at room temperature at pressures of 2.75 and 6.7 kbar. On the basis of the experimental data, the p-Tphase diagram for the first-order phase transitions has been plotted. The unusual shape of the phase diagram (a slow monotonic growth of the transition temperature with a slope dT/dp=4 deg/kbar followed by a sharp drop around the point p ₀=6.5 kbar, T ₀=324 K) has been analyzed using the Landau theory of second-order phase transitions. Our analysis supports the hypothesis of a second-order phase transition around this point and also exhibits satisfactory agreement between calculations and the experimental curves of the first-order phase transitions. Zh. éksp. Teor. Fiz. 115, 2190–2196 (June 1999)     

Explosive percolation in the human protein homology network

We study the explosive character of the percolation transition in a real-world network. We show that the emergence of a spanning cluster in the Human Protein Homology Network (H-PHN) exhibits similar features to an Achlioptas-type process and is markedly different from regular random percolation. The underlying mechanism of this transition can be described by slow-growing clusters that remain isolated until the later stages of the process, when the addition of a small number of links leads to the rapid interconnection of these modules into a giant cluster. Our results indicate that the evolutionary-based process that shapes the topology of the H-PHN through duplication-divergence events may occur in sudden steps, similarly to what is seen in first-order phase transitions.     

The influence of magnetoelastic interaction on structural phase transitions in cubic ferromagnetics

In the framework of the Landau theory of phase transitions, the influence of the magnetoelastic interaction on structural transitions in cubic ferromagnetics with a positive first magnetic anisotropy constant is analyzed. It is shown that structural transitions are not accompanied by a reorientation of magnetization in this case. The phase diagrams of such ferromagnetics either contain a termination point of the structural transition or a critical point in which the first-order transition is replaced by a second-order one. Magnetoelastic interaction also leads to the appearance of an interval of the ferromagnetic parameters in which a coupled first-order structural-magnetic transition exists. The phase T?x diagram for Heusler Ni_2+x Mn_1?x Ga alloys is calculated, which is in good agreement with the experimental phase diagram of these alloys.     

Phase transitions of two spin-1/2 Baxter–Wu layers coupled with Ising-type interactions

Using a Monte Carlo simulation and the single histogram reweighting technique,we study the critical behaviors and phase transitions of the Baxter-Wu(BW)model on a two-layer triangular lattice with Ising-type interlayer couplings.Via the finite-size analysis,we obtain the transition temperatures and critical exponents at repulsive and attractive interlayer couplings.The data for the repulsive interlayer coupling suggest continuous transitions,and the critical behaviors are the same as those of the 2D BW model,belonging to the four-state Potts universality class.The reduced energy cumulants and the histograms reveal that attractive coupling leads to weak firstorder phase transitions.The pseudocritical exponents with the existence of the interlayer couplings indicate that the first-order transition is very close to the critical point of the 2D standard BW model.     

Quantum phase transitions in the interacting boson model: integrability, level repulsion, and level crossing

We study the quantum phase transition mechanisms that arise in the interacting boson model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.     

Elastic phase transitions in metals at high pressures

The elastic phase transitions of cubic metals at high pressures are investigated within the framework of Landau theory. It is shown that at pressures comparable with the magnitude of the bulk modulus the phase transition is connected with the loss of stability relative to uniform deformation of the crystalline lattice. Discontinuity of the order parameter at the transition point and its equilibrium value are expressed through the second-?to fourth-order elastic constants. The second-,third-?and fourth-order elastic constants and phonon dispersion curves of vanadium under hydrostatic pressure are obtained by first-principles calculations. Structural transformation in vanadium under pressure is studied using the obtained results. It is shown that the experimentally observed at P?≈?69?GPa phase transition in vanadium is the first-order phase transition close to a second-order phase transition.     

Coulomb-frustrated phase separation phase diagram in systems with short-range negative compressibility

Using numerical techniques and asymptotic expansions we obtain the phase diagram of a paradigmatic model of Coulomb-frustrated phase separation in systems with negative short-range compressibility. The transition from the homogeneous phase to the inhomogeneous phase is generically first order in isotropic three-dimensional systems except for a critical point. Close to the critical point, inhomogeneities are predicted to form a bcc lattice with subsequent transitions to a triangular lattice of rods and a layered structure. Inclusion of a strong anisotropy allows for second- and first-order transition lines joined by a tricritical point.     

Magnetic phase transitions and the dynamic electric polarization in the LaMn<Subscript>2</Subscript>O<Subscript>5</Subscript> compound

Possible phase transitions to the ferromagnetic phase in the LaMn₂O₃ compound have been studied in the framework of a phenomenological approach based on a symmetry analysis. The conditions that parameters of the thermodynamic potential must satisfy to realize a second-order transition have been found. The line of the first-order phase transitions in this system and the critical point of the second-order phase transition line have been determined. It was shown that a dynamic electric polarization can form in the antiferromagnetic phase.     

Study of the first-order transition in the spin-1 Blume–Capel model by using effective-field theory

The spin-1 Blume–Capel model on a square lattice is studied by using an effective-field theory (EFT) with correlation. We propose an expression for the free energy within the EFT. The phase diagram is constructed in the temperature (T) and single-ion anisotropy amplitude (D) plane. The first-order transition line is obtained by Maxwell construction (comparison between free energies). Our results predict first-order transitions at low temperatures and large anisotropy strengths, which correspond in the phase diagram to the existence of a tricritical point (TCP). We compare our results with mean-field approximation (MFA), that show a qualitative correct behavior for the phase diagram.     

Structural phase transitions in ZnS

X-ray diffraction techniques have been used to investigate structural phase transitions in ZnS between 20 and 1200°C. These measurements imply that the transition from the cubic 3C structure to the hexagonal 2H structure is a first-order phase transition while transitions between the 2H, 4H, and the 6H(33) hexagonal structures were found to obey the symmetry rules of second-order phase transitions. Direct transitions from the cubic 3C structure to the 4 or 6H hexagonal structures are not observed.     

Smectic A-C-A Liquid Crystal Reentrance: A Photon Transmission Study

Ultraviolet/visible photon transmission measurements were applied to study liquid crystal phase transitions in the binary BOPDOB-BOPOOB mixture. A sequence exhibiting a new reentrant, namely isotropic-nematic-smectic A-C-A as temperature is lowered, is identified. For the smectic A-C transition, the critical exponent g is seen to cross over from the mean-field 0.501 - 0.008 to the helium-like 0.336 - 0.012 as the transition is approached. The reentrant C-A transition is first-order, signalling a tricritical point in the phase diagram.     

Phase transitions in liquid 3He

The phase transitions of liquid 3He are described by truncations of an exact nonperturbative renormalization group equation. The location of the first-order transition lines and the jump in the order parameter are computed quantitatively. At the triple point we find indications of partially universal behavior. We suggest experiments that could help to determine the effective interactions between fermion pairs.     

The kinetic spin-1 Blume-Capel model with Glauber dynamic

We study the dynamic phase transitions (DPT), within a mean-field approach, in the kinetic spin-1 Blume-Capel model by using the Glauber-type stochastic dynamics. The nature of the transition is characterized by investigating the behavior of the thermal variation of the dynamic order parameter and the Lyapunov exponent. The phase diagram is constructed in the temperatures (T) and single-ion anisotropy amplitude (D) plane. Our results predict first-order transitions at low temperature and large anisotropy strengths, which correspond in the phase diagram to the existence of a nonequilibrium tricritical point (TCP). We compare our results with the equilibrium phase diagram.     

Cascade of phase transitions in GdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

Cascade of phase transitions in GdFe₃(BO₃)₄ at 156, 37, and 9 K has been detected by specific heat measurements and further studied by Raman scattering and Nd³⁺ spectroscopic probe method. A weakly first-order structural phase transition at 156 K is followed by a second-order antiferromagnetic ordering phase transition at 37 K and a first-order spin-reorientational phase transition at 9 K.