Symmetry Restoring Phase Transitions at High Density in a 4D Nambu-Jona-Lasinio Model with a Single Order Parameter

High density phase transitions in a 4-dimensional Nambu-Jona-Lasinio model containing a single symmetry breaking order parameter coming from the fermion-antifermion condensates are researched and expounded by means of both the gap equation and the effective potential approach. The phase transitions are proven to be second-order at a high temperature T; however at T = 0 they are first- or second-order, depending on whether A/m(0), the ratio of the momentum cutoff A in the fermion-loop integrals to the dynamicalfermion mass m(0) at zero temperature, is less than 3.387 or not. The former condition cannot be satisfied in some models. The discussions further show complete effectiveness of the critical analysis based on the gap equation for second order phase transitions including determination of the condition of their occurrence.     

Top-Quark Condensate at Finite Temperature and Electroweak Symmetry Restoration

The gap equation at finite temperature in the top-quark condensate scheme of electroweak symmetry breaking is proven to have the identical form in both the imaginary and real time formalisms of thermal field theory. By means of the gap equation, combined with the basic relation to define the vacuum expectation value v of the effective Higgs field, we analyze the dependence on temperature T and chemical potential p of the dynamical top-quark mass as the order parameter characteristic of symmetry breaking, and obtain the p-T criticality curve for symmetry restoration. We find out that the critical temperature T_c = 2υ for μ = 0 and the critical chemical potential μ_c = 2 π υ / √3 for T = 0. When μ = 0, the top-quark mass near T_c has the leading (T_c² - T²)^1/2 behavior with an extra factor dependent on temperature T and the momentum cutoff Λ. However, it is generally argued that the symmetry restoration at T ≥ T_c is still a second-order phase transition.     

Thermomodulation experiments at the cubic-to-tetragonal phase transition in SrTiO3

After a brief comment on the important features of strontium titanate and a critical review of recent optical work in this material, thermoabsorption results at the cubic-to-tetragonal second-order phase transition are reported. Use of insulating samples has been possible by means of indirect heating. Optical evidence of the phase change is seen for the momentum-forbidden transitions starting at the indirect gap energy. This is discussed in terms of the relaxation of the momentum condition brought about by structural fluctuations near the transition temperature T₀. Part of the effect may be related to the increasing static distortion of the lattice in the tetragonal state. The results presented also confirm earlier pictures of the absorption threshold as due to LO-phonon-assisted Γ₁₅→X₃ transitions (with phonon energy equal to 52 meV). Furthermore, in the vicinity of T₀, an extra thermomodulation signal, corresponding to a weak absorption threshold ? 20 meV higher than the gap, becomes visible. This critical point is also particularly sensitive to the application of electric fields, as found by electroabsorption results obtained at liquid nitrogen temperature.     

Real-Time Thermal Field Theory Analyses of 2D Gross-Neveu Model

The discrete symmetry breaking and possible restoration at finite temperature T are analyzed in 20 Gross-Neveu model by the real-time thermal field theory in the fermion bubble approximation. The dynamical fermion mass m is proven to, be scale-independent and this fact indicates the equivalence between the fermion bubble diagram approximation and the meanfield approximation used in the auxiliary scalar field approach. Reproducing of the nonzero critical temperature T_c = 0.567m(O), m(0) is the dynamical fermion mass at T = 0, shows the equivalence between the real-time and the imaginary-time thermal. field theories in this problem. However, in the real-time formalism, more results including absence of scalar bound state, the equation of criticality curve of chemical potential-temperature and the ln(T_c/T) behavior of m² at T ≤ T_c can be easily obtained. The last one indicates the second-order phase transition feature of the symmetry restoration.     

Electrical Neutrality and Symmetry Restoring Phase Transitions at High Density in a Two-Flavor Nambu-Jona-Lasinio Model

A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe twoflavor normal quark matter. Depending on whether mo/A, the ratio of dynamical quark mass in vacuum and the 3D momentum cutoff in the loop integrals, is less or greater than 0.413, the phase transition will be of the second or first order. A complete phase diagram of u quark chemical potential versus mo is given. With the electrical neutrality constraint, the region where the second order phase transition happens will be wider than the one without electrical neutrality limitation. The results also show that, for the value of m0/∧ from QCD phenomenology, the phase transition must be of the first order.     

Coulomb interaction and first-order superconductor-insulator transition

The superconductor-insulator transition (SIT) in regular arrays of Josephson junctions is studied at low temperatures. We derived an imaginary time Ginzburg-Landau-type action properly describing the Coulomb interaction. The renormalization group analysis at zero temperature T=0 in the space dimensionality d=3 shows that the SIT is always of the first order. At finite T, a tricritical point separates the lines of the first- and second-order phase transitions. The same conclusion holds for d=2 if the mutual capacitance is larger than the distance between junctions.     

The mixed-spins 1/2 and 3/2 Blume—Capel model with a random crystal field

The random crystal field(RCF) effects are investigated on the phase diagrams of the mixed-spins 1/2 and 3/2 Blume-Capel(BC) model on the Bethe lattice.The bimodal random crystal field is assumed and the recursion relations are employed for the solution of the model.The system gives only the second-order phase transitions for all values of the crystal fields in the non-random bimodal distribution for given probability.The randomness does not change the order of the phase transitions for higher crystal field values,i.e.,it is always second-order,but it may introduce first-order phase transitions at lower negative crystal field values for the probability in the range about 0.20 and 0.45,which is only the second-order for the non-random case in this range.Thus our work claims that randomness may be used to induce first-order phase transitions at lower negative crystal field values at lower probabilities.     

Structural phase transitions during high-energy ball milling of BaTiO3

Microstructural characterization of ball milled perovskite BaTiO₃ powders has been done by the modeling of X-ray diffraction profiles. The study reveals that on size reduction, BaTiO₃ powders undergo a continuous, displacive, and diffusionless dynamic phase transitions involving tetragonal (T), monoclinic (M), and orthorhombic (O) symmetry via the second-order type [T?→?(T?+?M)?→?(M?+?O)?→?O] when stimulated by a high-power pulse of pressure in a planetary mill. The order parameter, a phenomenological quantity to describe the general behavior of a system going through phase transitions has been estimated using spontaneous strain calculated from lattice parameters or physical distortions derived from atomic coordinates or both. At room temperature, BaTiO₃ nanoparticle achieved an orthorhombic phase when a critical size (<15?nm) has been reached at later stage of milling (≥70?h). Raman's study reveals similar structural phase transitions sequence on size reduction and TEM study reveals the corresponding particle diameter.     

Critical Analyses of Order Parameter and Phase Transitions at High Density in Gross－Neveu Model

By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and some specJal first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proven that in D = 3 GN model a first order phase transition does occur in the case of zero temperature and finite chemical potential.     

Incommensurate magnetic order in TbTe3

We report a neutron diffraction study of the magnetic phase transitions in the charge-density wave (CDW) TbTe(3) compound. We discover that in the paramagnetic phase there are strong 2D-like magnetic correlations, consistent with the pronounced anisotropy of the chemical structure. A long-range incommensurate magnetic order emerges in TbTe(3) at T(mag1) = 5.78 K as a result of continuous phase transitions. We observe that near the temperature T(mag1) the magnetic Bragg peaks appear around the position (0, 0, 0.24) (or its rational multiples), that is fairly close to the propagation vector (0,0,0.29) associated with the CDW phase transition in TbTe(3). This suggests that correlations leading to the long-range magnetic order in TbTe(3) are linked to the modulations that occur in the CDW state.     

Magnetic Properties and magnetic phase diagrams of intermetallic compound GdMn2Ge2

A modified Yafet－Kittle model is applied to investigate the magnetic properties and magnetic phase transition of the intermetallic compound GdMn_2Ge_2. Theoretical analysis and calculation show that there are five possible magnetic structures in GdMn_2Ge_2. Variations of external magnetic field and temperature give rise to the first-order or second-order magnetic transitions from one phase to another. Based on this model, the magnetic curves of GdMn_2Ge_2 single crystals at different temperatures are calculated and a good agreement with experimental data has obtained. Based on the calculation, the H－T magnetic phase diagrams of GdMn_2Ge_2 are depicted. The Gd－Gd, Gd－Mn, intralayer Mn－Mn and interlayer Mn－Mn exchange coupling parameters are estimated. It is shown that, in order to describe the magnetic properties of GdMn_2Ge_2, the lattice constant and temperature dependence of interlayer Mn－Mn exchange interaction must be taken into account.     

Low-Temperature Phase Transitions in the Trigonal Modification of Cs 3 Bi 2 Br 9 and Cs 3 Sb 2 I 9

The trigonal (P-3 m1) modification of Cs 3 Bi 2 Br 9 and Cs 3 Sb 2 I 9 have been studied using NQR, X-ray single crystal and powder pattern methods. Moreover, the heat capacity was measured in a wide temperature interval: 4-300 K. In Cs 3 Bi 2 Br 9 a second-order phase transition was found at T C = 96 K. The low-temperature phase is monoclinic (C12/c1), with the unit cell doubled along the [001] direction. Cs 3 Sb 2 I 9 has a sequence of phase transitions at T C = 85 K, T i = 78 K and T L = 72.1 K. The monoclinic structure below 85 K is isomorphic with the low-temperature structure of Cs 3 Bi 2 Br 9 . According to calorimetric data the lock-in transition at 72.1 K is discontinuous.     

General holographic superconductor models with Born–Infeld electrodynamics

A general class of holographic superconductor models in Schwarzschild AdS black hole with the Born–Infeld electrodynamics is investigated. It is found that the Born–Infeld coupling parameter affects the critical temperature, the order of phase transitions, the conductivity and the critical exponents near the second-order phase transition point. It is also noted that both the position of the conductivity coherence peak and the ratio of the gap frequency in conductivity to the critical temperature depend on the model parameters and the Born–Infeld coupling parameter.     

Ferroelectric phase transition in Ga2Te3 single crystals

Measurements of the electrical conductivity and Hall effect were carried out in a wide temperature range (200-500 K) for Ga₂Te₃ crystals. The crystals were grown in single crystalline form by making a modification of the travelling heater method technique. The measurements revealed unusual observations in the electric conductivity and Hall mobility indicating the presence of some type of phase transitions at about 430 K. So, ferroelectric behavior was examined for confirming the presence of second-order (ferroelectric) phase transition. An energy gap of 1.21 eV and depth of the impurity center of 0.11 eV were found.     

Transformation of the short-range order upon melting of Cu<Emphasis Type="Italic">Hal</Emphasis> nanocrystals in glasses

The reduced density of states at the edge of interband transitions in CuCl and CuBr nanocrystals is described by a step at T → 0. As the temperature increases, the step is smeared toward the band gap and the long-wavelength absorption tail agrees with the Urbach rule. A change in the phase state of CuCl or CuBr nanoparticles (the crystal-melt transition) is accompanied by an insignificant change in the band gap, and the long-wavelength absorption tail for the interband transitions considerably extends deeper into the band gap as compared to that for crystals at the same temperature. The change observed in the band gap upon melting is explained by the transformation of short-range order in CuCl and CuBr melts. An increase in thermal smearing of the long-wavelength absorption tail for nanomelts is associated with the severalfold increase in the amplitude of thermal fluctuations of the band gap, possibly, due to the disappearance of the long-range order in the melts. A lower melting temperature of large (>30 nm) CuCl and CuBr particles as compared to the melting temperature of bulk samples indicates the presence of the second component NaCl or NaBr. Consequently, the CuCl-NaCl and CuBr-NaBr eutectic nanosystems undergo melting and crystallization. A small shift in the band gap observed in this case upon melting confirms the conclusion drawn by Zalkin that eutectic melts have a microheterogeneous structure.     

Dynamic phase transitions in a cylindrical Ising nanowire under a time-dependent oscillating magnetic field

The dynamic phase transitions in a cylindrical Ising nanowire system under a time-dependent oscillating external magnetic field for both ferromagnetic and antiferromagnetic interactions are investigated within the effective-field theory with correlations and the Glauber-type stochastic dynamics approach. The effective-field dynamic equations for the average longitudinal magnetizations on the surface shell and core are derived by employing the Glauber transition rates. Temperature dependence of the dynamic magnetizations, the dynamic total magnetization, the hysteresis loop areas and the dynamic correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic transitions as well as the dynamic phase transition temperatures and the compensation behaviors. The system strongly affected by the surface situations. Some characteristic phenomena are found depending on the ratio of the physical parameters in the surface shell and the core. According to the values of Hamiltonian parameters, five different types of compensation behaviors in the Néel classification nomenclature exist in the system. The system also exhibits a reentrant behavior.     

Fractional phase transitions of RN-AdS black holes at their Davies points

In this study, we investigate the phase transitions of the RN-AdS black hole at its Davies points according to the generalized Ehrenfest classification of phase transition established based on fractional derivatives. Notably, Davies points label the positions at which the heat capacity diverges. According to the usual Ehrenfest classification, second-order phase transitions occur at these points. For the RN-AdS black hole, the Davies points can be classified into two types. The first type corresponds to extreme values of the temperature, and the second type corresponds to the infection point (namely the critical point) of temperature. Employing the generalized Ehrenfest classification, we determine that the orders of phase transition at the two types of Davies points are different, that is, we note an order of 3/2 for the first type and 4/3 for the second type. Thus, this finer-grained classification can discriminate between phase transitions that are expected to lie in the same category, providing new insights leading toward a better understanding of black hole thermodynamics.     

Phase separation of binary systems

In this paper, three physical predictions on the phase separation of binary systems are derived based on a dynamic transition theory developed recently by the authors. First, the order of phase transitions is precisely determined by the sign of a nondimensional parameter K such that if K>0, the transition is first order with latent heat and if K<0, the transition is second order. Here the parameter K is defined in terms of the coefficients in the quadratic and cubic nonlinear terms of the Cahn-Hilliard equation and the typical length scale of the container. Second, a phase diagram is derived, characterizing the order of phase transitions, and leading in particular to a prediction that there is only a second-order transition for molar fraction near 1/2. This is different from the prediction made by the classical phase diagram. Third, a TL-phase diagram is derived, characterizing the regions of both homogeneous and separation phases and their transitions.     

Phase diagram and critical end point for strongly interacting quarks

We introduce a method based on chiral susceptibility, which enables one to draw a phase diagram in the chemical-potential-temperature plane for strongly interacting quarks whose interactions are described by any reasonable gap equation, even if the diagrammatic content of the quark-gluon vertex is unknown. We locate a critical end point at (μ(E),T(E))～(1.0,0.9)T(c), where T(c) is the critical temperature for chiral-symmetry restoration at μ=0, and find that a domain of phase coexistence opens at the critical end point whose area increases as a confinement length scale grows.     

Quantum stabilization in anharmonic crystals

For a model of interacting quantum particles of mass m oscillating in a double-well crystalline field, a mechanism of its stabilization by quantum effects is described. In particular, a stability condition involving m, the interaction intensity, and the parameters of the crystalline field is given. It is independent of the temperature and is satisfied if m is small enough and/or the tunneling frequency is big enough. It is shown that under this condition the infinite-volume free energy density is an analytic function of the external field and the displacement-displacement correlation function decays exponentially; hence, no phase transitions can arise at all temperatures. This gives a complete and rigorous answer to the question about the influence of quantum effects on structural phase transitions, the discussion of which was initiated in [T. Schneider, H. Beck, and E. Stoll, Phys. Rev. B 13, 1123 (1976)]].