Low-energy theorems of hot and dense QCD in a magnetic field

The nonperturbative QCD vacuum at finite temperature and a finite baryon density in an external magnetic field is studied. Equations that relate nonperturbative condensates to the thermodynamic pressure for T ≠ 0, μ _q ≠ 0, and H ≠ 0 are obtained, and low-energy theorems are derived.     

Phase structure of the linear sigma model with the standard symmetry breaking term

The linear sigma model at finite isospin chemical potential μ and temperature T is systematically studied by means of the Cornwal–Jackiw–Tomboulis (CJT) effective potential calculated in the improved Hartree–Fock (HF) approximation, where the Goldstone theorem and the thermodynamic consistency are respected. It results that in the chiral limit, for μ=0 the chiral phase transition is second order as expected from the general universality arguments, and for μ≠0 the phase diagram for the pion condensation in the (T,μ) plane exhibits a tricritical point which is crossover from first-order to second-order phase transitions. In the physical world, where the chiral symmetry is explicitly broken, the pion condensation occurs at μ=m _π , the pion mass in vacuum, and its phase diagram is basically in agreement with those found from the chiral perturbation theory. The chiral symmetry gets restored at high values of T for fixed μ and of μ for fixed T.     

Variations in the electrical resistivity of La0.67Ca0.33MnO3 films and induced interconversions of ferromagnetic and nonferromagnetic inclusions in their bulk

A significant (∼1.8%) positive unit between the parameters of the crystal lattice is the reason of tetragonal distortion (a _⊥/a _‖ ≈ 1.04) and reduction in the volume of the unit cell of La_0.67Ca_0.33MnO₃ films (15 nm) quasicoherently grown on the (001) surface of a LaAlO₃ substrate. The films consist of single-crystal blocks with the lateral size of 30–50 nm. The atomically smooth LaAlO₃-La_0.67Ca_0.33MnO₃ interphase boundary has no misfit dislocations. At T = 4.2 K, the transformation of nonferromagnetic phase inclusions into ferromagnetic ones in a constant magnetic field H is accompanied by a stable reduction in the electrical resistivity ρ of manganite films with time, so that the curve ρ(t) is well approximated by the relationship ρ(t) ∼ ρ₁(t − t ₀)^1/2, (where t ₀ is the time for establishment of the specified value (μ₀ H = 5 T) of the magnetic field and ρ₁ is a coefficient independent of H). The magnetocrystalline anisotropy due to the elastic deformation of films by the substrate and stratification of electronic phases are the reasons of the distinct hysteresis in the dependences ρ(μ₀ H, T < 100 K) obtained on μ₀ H scanning in the sequence 5 T → 0 → −5 T → 0 → 5 T. At T = 50 K and μ₀ H = 0.4 T, the magnetoresistance MR = 100% [ρ(μ₀ H) − ρ(μ₀ H = 0)]/ρ(μ₀ H = 0) of LCMO films attains 150%.     

Phase transition in three-dimensional quantum electrodynamics at <Emphasis Type="Italic">T</Emphasis> ≠ 0

Dynamic mass generation in 3D quantum electrodynamics (QED₃) is considered at T ≠ 0. To solve the Schwinger–Dyson equation for the Matsubara electron Green’s function, the ladder approximation is used and the corresponding photonic function is taken in the Landau gauge. In this case, the instant approximation is used for the photonic function. It is established that the process of dynamical mass generation in QED₃ at T ≠ 0 is accompanied by a phase transition. Formal analogy of transitions in the coupling constant is revealed at T ≠ 0 in QED₃, at T = 0 in QED₄, and in graphene theory. Critical values of the coupling constant and temperature, calculated numerically based on an approximate analytical solution of the Schwinger–Dyson equation are of the same orders of magnitude.     

Electro- and magnetotransport in La0.67Ba0.33MnO3 nanosized films coherently grown on a vicinally polished (LaAlO3)0.29 + (SrAl0.5Ta0.5O3)0.71 substrate

The structure, orientation, and the response of electroresistance to magnetic field H and varying temperature T have been studied for 30-nm-thick La_0.67Ba_0.33MnO₃ (LBMO) films. The deviation of the [001] direction in manganite layers from the normal to the plane of the (LaAlO₃)_0.29 + (SrAl_0.5Ta_0.5O₃)_0.71 substrate strictly corresponds to the vicinal angle of the latter. The minimum yield determined from 227-keV proton scattering spectra is 0.025, signifying a high order of the cationic sublattice in the films. The biaxial compression of stable nuclei of the manganite phase affects their stoichiometry, thus contributing to the depletion of LBMO films in the alkaline-earth element. The maximum electroresistance values have been observed in the films grown at T _max ≈ 320 K, a temperature about 20 K lower than the Curie temperature of the corresponding bulk single crystals, and the maximum magnetoresistance (MR ≈ −0.42, μ₀ H = 2 T) occurs at T ≈ 300 K. At low temperatures (T < T _max/3) and μ₀ H < 0.45 T, the electroresistance response of LBMO films to a magnetic field materially depends on the anisotropic magnetoresistance and the intensity of hole scattering from domain walls; when μ₀ H > 0.5 T, the major current-carrier relaxation mechanism is the interaction with magnons.     

Anisotropic magnetoresistance of partially relaxed SrRuO3 films

The SrRuO₃ films (50 nm thick) grown by laser evaporation on (001)(LaAlO₃)_0.3 + (Sr₂AlTaO₆)_0.7 substrates were under partially relaxed biaxial compressive mechanical stresses. The films consisted of crystallites with lateral dimensions of 40–100 nm and a relative azimuthal misorientation of about 0.9°. Ferromagnetic ordering of spins in the SrRuO₃ films was manifested by a change in the slope of the temperature dependence of their electrical resistivity ρ at T ≈ 155 K. For a magnetic field H parallel to the measuring current, the maximum values (∼7.5%) of the magnetoresistance MR = [ρ(μ₀ H = 5 T) − ρ(μ₀ H = 0)]/ρ(μ₀ H = 0) were observed at temperatures of about 100 K. At T = 95 K (μ₀ H = 5 T), the anisotropic magnetoresistance of the films was 8% and increased by a factor of approximately 1.5 with decreasing temperature to 4.2 K.     

Properties of superconducting Nb/Al/Nb/Al?AlOx?Al?AlOx?Al/Nb/Al/Nb tunnel junctions

Modified geometry (MG) devices, Nb/Al/Nb/Al−AlO_x−Al−AlO_x−Al/Nb/Al/Nb, have been fabricated and investigated in comparison with the basic geometry (BG) double-barrier Nb/Al−AlO_x−Al−AlO_x−Al/Nb devices. The enhancement of the critical temperature in the Al film is found to be weaker for the MG devices as compared with the BG devices at temperatures nearT=4.2 K but stronger at lowT. Indication of an enhancement of dc Josephson critical current density,j _c , at bias voltageV≠0 as compared withj _c (V=0) has been observed in the MG devices for the first time.     

Oscillations and quantization of resistance at the temperature critical points of PbS-PbTe-PbS three-layer films on (001) KCl

Oscillations and a set of inflection points have been discovered in the temperature dependences of the resistance of single-crystal PbS-PbTe-PbS three-layer films on (001) KCl. Extrema and inflection points are observed at the temperatures (m/n)T ₀ (T ₀=5.238 K), and at these temperature critical points the resistance of the samples takes one of the values (p/q)R _Q , where R _Q =25812.8 Ω is the resistance quantum; and m, n, p, and q are integers. Fiz. Tverd. Tela (St. Petersburg) 41, 1693–1697 (September 1999)     

NMR relaxation times and proton motion in HxWO3

The relaxation timesT ₁,T _1q,T _1D, andT ₂ for¹H in the tetragonal-A phase of H_xWO₃ have been measured over the temperature range 190 to 490 K. The¹H relaxation behaviour appears to be governed by diffusion over inequivalent jump distances, approximating to a short range planar diffusion and a long range isotropic diffusion. Parameters for the latter motion are estimated asE _a = 68 kJ/mol and ₀=2.5×10^–13 s. The powder X-ray diffraction pattern for this phase of H_xWO₃ has been studied over the temperature range 300–470 K. The tetragonal distortion diminishes with temperature and H_0.43 WO₃ becomes cubic at about 435 K. Volumetric studies of hydrogen evolution show that decomposition accelerates at approximately this temperature.     

Metastable Behavior for Bootstrap Percolation on Regular Trees

We examine bootstrap percolation on a regular (b+1)-ary tree with initial law given by Bernoulli(p). The sites are updated according to the usual rule: a vacant site becomes occupied if it has at least θ occupied neighbors, occupied sites remain occupied forever. It is known that, when b>θ≥2, the limiting density q=q(p) of occupied sites exhibits a jump at some p _T=p _T(b,θ)∈(0,1) from q _T:=q(p _T)<1 to q(p)=1 when p>p _T. We investigate the metastable behavior associated with this transition. Explicitly, we pick p=p _T+h with h>0 and show that, as h ↓0, the system lingers around the “critical” state for time order h ^−1/2 and then passes to fully occupied state in time O(1). The law of the entire configuration observed when the occupation density is q∈(q _T,1) converges, as h ↓0, to a well-defined measure.     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

Deconfinement transition for nonzero baryon density in the field correlator method

Deconfinement phase transition due to the disappearance of confining colorelectric field correlators is described using a nonperturbative equation of state. The resulting transition temperature T _c (μ) at any chemical potential μ is expressed in terms of the change of the gluon condensate ΔG ₂ and absolute value of the Polyakov loop L _fund(T _c ), which is known from the lattice and analytic data, and is in good agreement with the lattice data for ΔG ₂ ≈ 0.0035 GeV⁴; e.g., T _c (0) = 0.27, 0.19, and, 0.17 GeV for n _f = 0, 2, and 3, respectively. The text was submitted by the authors in English.     

Gaussian Random Matrix Models¶for q-deformed Gaussian Variables

We construct a family of random matrix models for the q-deformed Gaussian random variables G _μ=a _μ+a^*_μ, where the annihilation operators a _μ and creation operators $a\gwia_\nu$ fulfill the $q$-deformed commutation relation a _μ a^*_ν−q a^*_ν a _μ=Γ_μν, Γ_μν is the covariance and 0<q<1 is a given number. An important feature of the considered random matrices is that the joint distribution of their entries is Gaussian. Received: 29 March 2000 / Accepted: 1 August 2000     

The 2<Superscript>1/3</Superscript> rule for magnetic susceptibility of gadolinium

The dependences of the magnetization M and the magnetic susceptibility χ = ∂M/∂H of pure gadolinium (the concentration of foreign impurities is lower than 0.1 wt %) on the temperature T and the magnetic field H have been measured using a Quantum Design MPMS-5XL SQUID magnetometer. In this material, inhomogeneities of the atomic structure should not lead to a nonuniform distribution of the magnetic characteristics (including the Curie temperature T _C) over the volume of the sample. The obtained dependences of M and χ have been used to investigate the possibility of suppressing magnetic inhomogeneities of other types by magnetic fields with a strength of up to 50 kOe. It has been assumed that these inhomogeneities are suppressed when the specific relationship, namely, the 2^1/3 rule is fulfilled. The rule relates the portions of the dependence χ(T, H) which at the temperature T = T _C and at the maximum in the curve χ(T) (T = T _m ) depend on H in accordance with the H ^2/3 law. It has been shown that the portions separated from the experimental curves χ(T _C, H) and χ(T _m , H) obey the 2^1/3 rule.     

Electronic-transport properties of unhydrogenated amorphous gallium arsenide

Summary Hall mobility, μ_H, and electrical conductivity, σ, of unhydrogenated amorphous-gallium-arsenide films, prepared by r.f. sputtering, have been measured. Conductivity as a function of temperature shows a variable-range hopping mechanism atT<260 K, while at high temperature, conductivity and Hall mobility are both thermally activated. The results are interpreted in terms of the presence of defect complexes due to an excess of Ga. The stoichiometry and the structure of the films are used to explain the behaviour and the values of μ_H. The values of the activation energy of the conductivity seem in agreement with theoretical calculations on the position of electronic states created by defect complexes in the mobility-gap of a-GaAs.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Probing the field-induced variation of the chemical potential in Bi2Sr2CaCu2Oy via magneto-thermopower measurements

Approximating the shape of the magneto-thermoelectric power (TEP) ΔS(T,H) measured in Bi₂Sr₂CaCu₂O_y by an asymmetric linear triangle of the form ΔS(T,H)≃S _p (H)±B ^±(H)(T _c −T) with positive B ⁻(H) and B ⁺(H) defined below and above T _c , we observe that B ⁺(H) ≃2B ⁻(H). To account for this asymmetry, we explicitly introduce the field-dependent chemical potential μ(H) of holes into the Ginzburg-Landau theory and calculate both an average ΔS _av(T,H) and fluctuation contribution ΔS _fl(T,H) to the total magneto-TEP ΔS(T,H). As a result, we find a rather simple relationship between the field-induced variation of the chemical potential in this material and the above-mentioned magneto-TEP data around T _c , viz. Δ μ(H)∝S _p (H). Zh. éksp. Teor. Fiz. 116, 257–262 (July 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Nonperturbative approach to chiral phase transition in chromodynamics

A nonperturbative approach aimed at the localization of the QCD chiral phase transition atT, π≠0 is presented. We identify this transition with the dynamical quark mass peculiarity which results from the selfconsistent solution of the Schwinger-Dyson equation for the quark propagator. The specific model of the effective quark-gluon interaction, based both on the peculier interpolation for the running coupling constant and on the nonperturbative gluon magnetic and electric masses is exploited. The numerical estimates of the phase diagram are presented and it is shown that phase peculiarities are determined not only by the ultraviolet properties of QCD but also by its infrared structure. The obtained results are discussed, compared with other approaches and a possible interpretation is given.     

Strong coupling in the Kondo problem in the low-temperature region

The magnetic field dependence of the average spin of a localized electron coupled to conduction electrons with an antiferromangetic exchange interaction is found for the ground state. In the magnetic field range μH∼0.5T _c (T _c is the Kondo temperature) there is an inflection point, and in the strong magnetic field range μH≫T _c , the correction to the average spin is proportional to (T _c /μ H)². In zero magnetic field, the interaction with conduction electrons also leads to the splitting of doubly degenerate spin impurity states. Zh. éksp. Teor. Fiz. 115, 1263–1284 (April 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor     

Ferrimagnetic phase transition in the system Li0.5Fe2.52−x GaxO4 in the vicinity of the multicritical point of the x-T phase diagram

In connection with the problem of identifying magnetic states in the vicinity of x ₀ (the multicritical point of the x-T diagrams of spin-glass systems) a study has been made of properties that can be exploited to determine the presence of a thermodynamic phase transition at the Curie point T _C and the distinctive features of the transition, specifically, the temperature dependence of the magnetic part of the specific heat C _m(T), the temperature dependence of the low-field magnetization σ _H(T), and (with a view toward examining critical behavior in a magnetic field) the magnetization isotherms σ _H(T). The investigated object is the system of dilute ferrimagnetic spinels Li_0.5Fe_2.5−x Ga_xO₄, in which every type of magnetic state has spatially inhomogeneous cluster structures. The results obtained for a sample with x=1.45 indicate that the classical criteria of a ferrimagnetic second-order phase transition at T _C=(97±2) K occur for x∼x ₀. The results of similar investigations for a sample with x=1.6, which exists in the cluster spin-glass state for T<T _f=22 K and in an uncorrelated cluster state of the superparamagnetic type for T>T _f, are also given for comparison with the preceding case. Zh. éksp. Teor. Fiz. 114, 2065–2077 (December 1998)