Correlations in inhomogeneous Ising models

Using general methods developed in a previous treatment we study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings can vary both in strength and sign such that the coupling distribution is translationally invariant in diagonal direction. We calculate correlations parallel to the layering in the diagonally layered model with periodv=2, the so-called “general square lattice” model (GS). If the model has a finite critical temperature,T _c>0, we have a spontaneous magnetization belowT _c vanishing atT _c with the Ising exponent β=1/8. AtT _c correlations decay algebraically with critical exponnet η=1/4 and exponentially forT>T _c. In the frustrated case we have oscillatory behaviour superposed on the exponential decay where the wavevector of the oscillations changes at some “disorder temperature”T _D(>T _c) from commensurate to temperature-dependent in commensurate periods. If the critical temperature vanishes,T _c=0 we always have exponential decay at finite temperatures, while atT=T _c=0 we encounter either long-range order or algebraic decay with critical index η=1/2, i.e.T=0 is thus a critical point.     

Dynamic anomaly in the glass transition region of orthoterphenyl

We report on incoherent and coherent neutron scattering results in the supercooled liquid and the glassy regime of the van der Waals fluido-terphenyl using the backscattering and spin echo technique, respectively. A critical comparison of both techniques is presented. The data are analysed in the time domain assuming that microscopic correlation times (τ) scale with the viscosity η according to τ(T)～η(T)/T. With this assumption we obtain an agreement with several predictions of mode coupling theory: the existence of a critical temperatureT _c is shown, independently for both incoherent and coherent data, by a cusp in the temperature dependence of the Debye-Waller factorf _Q (T). BelowT _c f_Q(T) follows the predicted \(\sqrt {T_c - T} \) behaviour yielding also theQ-dependence of the critical parametersf _Q ^c andh _Q . AboveT _c the α-process or structural relaxation can be well parametrized by a stretched exponential function. In accordance with theory the structural relaxation curves can also be described by a power law with a critical (von Schweidler) exponentb=0.525±0.10.     

Solutions for the T = 0 quantum spin glass transition in a metallic model with spin-charge coupling

We solve several low temperature problems of an infinite range metallic spin glass model. A compensation problem of T 0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of δJ = J – J_c (T = 0). The critical value J_c(T = 0) = 3/16p_F^?1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica-overlap order parameter 〈Q^ab〉, a ≠ b, the diagonal 〈Q^aa〉 is confirmed as order parameter by the result 〈Q^aa〉 _SP ～ (δJ)^β, β = 1, and its susceptibility χ^aaaa ～(-δJ)^?γ with γ = 1/2 at T = 0. The value for γ agrees with the one for the transverse field Ising spin glass. The low γ decay of 〈Q^aa〉, ～ T is obtained exactly in the whole quantum disordered phase including the critical value.     

Interaction effects on atomic laboratory trapped Bose-Einstein condensates

We discuss the effect of inter-atoms interactions on the condensation temperature T _c of an atomic laboratory trapped Bose-Einstein condensate. We show that, in the mean-field Hartree-Fock and semiclassical approximations, interactions produce a shift Δ T _c /T _c ⁰ ≈ b ₁(a/λ _{T c} ) + b ₂(a/λ _{T c} )² + ψ[a / λ _{T c} ] with a the s-wave scattering length, λ _T the thermal wavelength and ψ[a / λ _{T c} ] a non-analytic function such that ψ[0] = ψ′[0] = ψ′′[0] = 0 and |ψ′′′[0]| = ∞. Therefore, with no more assumptions than Hartree-Fock and semiclassical approximations, interaction effecs are perturbative to second order in a / λ _{T c} and the expected non-perturbativity of physical quantities at critical temperature appears only to third order. We compare this finding with different results by other authors, which are based on more than the Hartree-Fock and semiclassical approximations. Moreover, we obtain an analytical estimation for b ₂ ? 18.8 which improves a previous numerical result. We also discuss how the discrepancy between b ₂ and the empirical value of b ₂ = 46 ± 5 may be explained with no need to resort to beyond-mean field effects.     

Modeling of the out-of-plane resistivity of cuprate superconductors

The out-of-plane (c-axis) resistivity, ρ_c(T), of high-T_c cuprates have been modeled in this study. The non-Fermi liquid like temperature dependence of ρ_c(T) has been described by considering (i) the full impact of the pseudogap (PG) in the electronic density of states (EDOS) and (ii) the presence of a quantum critical point (QCP) beneath the superconducting dome at slightly overdoped region. This simple phenomenological model describes the experimental ρ_c(T) data over a wide range of hole content (from the underdoped to slightly overdoped regions) remarkably well. The PG energy scale, ε_g (dominated by the anti-nodal parts of the Brillouin zone) extracted from the analysis of ρ_c(T) data was found to decrease almost linearly with increasing hole concentration, p, in the CuO₂ planes. We have also discussed about the possible origin of more conventional behavior of ρ_c(T) observed in the deeply overdoped side of the T–p phase diagram in this paper.     

Melting and elastic shear instability of alkali halides

Ultrasonic data for the elastic moduli c_ij as functions of pressure and temperature are used to calculate critical temperatures T_cr(P = 0) and their initial pressure derivatives (?T_cr/?P)_P=0 for the elastic stability of the alkali halides with the rocksalt and CsCl structures. The stability criteria used for the two structures are c′ = ½(c₁₁ ? c₁₂) = 0 and c₄₄ = 0, respectively. The critical parameters T_cr(P = 0) and (?T_cr/?P)_P=0 exhibit remarkable correlations with the melting temperatures T_m(P = 0) and their initial pressure derivatives (?T_m/?P)_P=0, offering strong support to the existence of a connexion between shear instability and melting, as postulated by previous investigators. Critical parameters for the rocksalt oxides MgO, CaO, and SrO compare favourably with the critical and melting parameters for their fluoride analogues LiF, NaF and KF respectively.     

Crossover scaling,correlation function and connectivity in dilute low temperature ferromagnets

For quenched dilute ferromagnets with a fractionp of spins (nearest neighbor exchange energyJ) and a fraction 1 —p of randomly distributed nonmagnetic atoms, a crossover assumption similar to tricritical scaling theory relates the critical exponents of zero temperature percolation theory to the low temperature critical amplitudes and exponents near the critical lineT _c (p)>0. For example, the specific heat amplitude nearT _c (p) is found to vanish, the susceptibility amplitude is found to diverge forT _c (p →p _c ) → 0. (Typically,p _c =20%.) AtT=0 the spin-spin correlation function is argued from a droplet picture to obey scaling homogeneity but (at fixed distance) not to vary like the energy; instead it varies as const + (p _c —p)^2β +? for fixed small distances. A generalization of the correlation function to finite temperatures nearT _c (p) allows to estimate the number of effective percolation channels connecting two sites in the infinite (percolating) network forp>p _c ; this in turn gives, via a dynamical scaling argument, a good approximation for theT=0 percolation exponent 1.6 in the conductivity of random three-dimensional resistor networks. This channel approximation also givesΦ=2 for the crossover exponent; i.e. exp(?2J/kT _c (p)) is an analytic function ofp nearp=p _c . An appendix shows that cluster-cluster correlations atT=0 (excluded volume effects) are responsible for the difference between percolation exponents and the (pure) Ising exponents atT _c (p=1).     

Temperature Dependence of the Upper Critical Field in Disordered Hubbard Model with Attraction

We study disorder effects upon the temperature behavior of the upper critical magnetic field in an attractive Hubbard model within the generalized DMFT+Σ approach. We consider the wide range of attraction potentials U—from the weak coupling limit, where superconductivity is described by BCS model, up to the strong coupling limit, where superconducting transition is related to Bose–Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures significantly higher than superconducting transition temperature, as well as the wide range of disorder—from weak to strong, when the system is in the vicinity of Anderson transition. The growth of coupling strength leads to the rapid growth of H_c2(T), especially at low temperatures. In BEC limit and in the region of BCS–BEC crossover H_c2(T), dependence becomes practically linear. Disordering also leads to the general growth of H_c2(T). In BCS limit of weak coupling increasing disorder lead both to the growth of the slope of the upper critical field in the vicinity of the transition point and to the increase of H_c2(T) in the low temperature region. In the limit of strong disorder in the vicinity of the Anderson transition localization corrections lead to the additional growth of H_c2(T) at low temperatures, so that the H_c2(T) dependence becomes concave. In BCS–BEC crossover region and in BEC limit disorder only slightly influences the slope of the upper critical field close to T _c . However, in the low temperature region H_c2 (T may significantly grow with disorder in the vicinity of the Anderson transition, where localization corrections notably increase H_c2 (T = 0) also making H_c2(T) dependence concave.     

Phase space analysis of interacting dark energy in f(T) cosmology

In this paper, we examine the interacting dark energy model in f(T) cosmology. We assume dark energy as a perfect fluid and choose a specific cosmologically viable form f(T) = ????T. We show that there is one attractor solution to the dynamical equation of f(T) Friedmann equations. Further we investigate the stability in phase space for a general f(T) model with two interacting fluids. By studying the local stability near the critical points, we show that the critical points lie on the sheet u* = (c ? 1)v* in the phase space, spanned by coordinates (u, v, ??, T). From this critical sheet, we conclude that the coupling between the dark energy and matter c ?? (?2, 0).     

Superconducting and magnetic properties of La3−x In Cex

Measurements of the critical temperature, T_c(x), the critical field, H_c2(x,T) and the susceptibility, χ (T), as a function de la concentration, x, in the system La₃₋x Ce_xIn, are compared with the theories of Muller-Hartmann and Zittsrtz, and Abrikosov and Gor'kov. The H_c2(x, T = 0) and χ(T) measurements indicate the appearance of short range antiferromagnetic order around x = 0.04 which is probably responsible for the anomalous behavior of T_c(x).     

Observation of a transition from BCS to HTSC-like superconductivity in Ba1 − x KxBiO3 single crystals

The temperature dependences of the upper critical field B _c2(T) and surface impedance Z(T) = R(T) + iX(T) have been measured in Ba_{1 ? x} K_xBiO₃ single crystals with transition temperatures 6 ≤ T _c ≤ 32 K (0.6 > x > 0.4). A transition from the BCS to an unusual type of superconductivity has been revealed: B _c2(T) curves of the crystals with T _c > 20 K have positive curvature (as in some HTSCs), and those of the crystals with T _c < 15 K described by the usual Werthamer-Helfand-Hohenberg (WHH) formula. The R(T) and X(T) dependences of the crystals with T _c ≈ 32 K and T _c ≈ 11 K in the temperature range T ? T _c are linear (as in HTSCs) and exponential (BCS), respectively. The experimental results are discussed using the extended saddle point model by Abrikosov.     

Critical and triple point temperatures of the first adsorbed layer of nitric oxide on graphite,boron nitride and lamellar halides

The two-dimensional critical temperature T_c(2D) of the first layer of nitric oxide adsorbed on homogeneous surfaces of graphite, boron nitride, cadmium halides (CdI₂, CdBr₂, CdCl₂) and magnesium bromide has been determined as accurately as possible. A correlation curve between T_c(2D) and the adsorbent crystalline parameter is compared to the correlation curve of this parameter with the two-dimensional triple point temperature T_t(2D) of the same layer on the above substrates and on those previously investigated by Enault and Larher. It appears from this comparison that T_c(2D) is less sensitive than T_t(2D) to the nature of the substrate: the difference between the extreme values of T_c(2D) is 25 K, whereas it is larger than 70 K for T_t(2D). Moreover the lowest values of T_c(2D) correspond to the substrates for which the lowest values of T_t(2D) have also been observed, namely graphite and boron nitride, both standing out by the smoothness of the adsorption potential of their cleavage faces. Furthermore we are led to reconsider the nature of the less dense phase (α phase) which hitherto has been inferred to be a 2D solid essentially composed of dimers lying flat on the surface.     

Superconducting behavior of amorphous Zr70Cu30

Measurement of the Meissner penetration depth, λ(T) were made in amorphous Zr₇₀Cu₃₀ samples. The results indicate that this amorphous alloy behaves as a BCS superconductor with 2Δ(0)?kT_c = 3.8, where Δ(0) is the superconducting energy gap at T=0 and T_c the critical temperature. It is also concluded that the low energy excitation, TLS, characteristics of amorphous material does not contribute to T_c.     

New expression for the partition function of a two-dimentional classical plasma

A new expression is derived for the canonical partition function Q of a two-dimentional Coulomb system. As a by-product Q is shown to exist above the critical temperature T_c for the collapse of a pair of opposite point charges.     

Size Dependences of the Magnetic Properties of Superconducting Lead–Porous Glass Nanostructures

Superconducting structures Pb–PG formed by filling a porous glass matrix with the lead from melt under pressure have been investigated. Samples with characteristic pore structure diameters of d ≈ 7, 3, and 2 nm have been studied. It has been found that the critical temperature of the superconducting transition in the samples under study is similar to the corresponding value T_c ≈ 7.2 K for bulk lead. At the same time, it has been observed that the critical magnetic field of the nanocomposites, which attains H_c(T = 0 K) ≈ 165 kOe for Pb–PG (3 nm), exceeds several times the value H_c(0) = 803 Oe for bulk lead. The low-temperature magnetic- field dependences of magnetic moment M(H) contain quasi-periodic flux jumps, which vanish with a decrease in the lead nanostructure diameter. A qualitative model of the observed effects is considered.     

Large upper critical field in non-centrosymmetric superconductor Y2C3

We determine the upper critical field μ₀H_c2(T_c) of non-centrosymmetric superconductor Y₂C₃ using two distinct methods: the bulk magnetization M(T) and the tunnel-diode oscillator (TDO) based impedance measurements. It is found that the upper critical field reaches a value of 30 T at zero temperature which is above the weak-coupling Pauli paramagnetic limit. We argue that the observation of such a large μ₀H_c2(0) in Y₂C₃ could be attributed to the admixture of spin-singlet and spin-triplet pairing states as a result of broken inversion symmetry.     

Equation of state for rotating nuclei at finite temperature

The equation of state ω(T, I) is derived for temperatures in the range0 ? T ? 0.5 MeV and spins in the range 0 ? I ? 24. It is demonstrated that if the yrast line backbends, then the equation of state contains a critical point at temperature T_c, and that backbending disappears for T > T_c.     

Fractional charges at finite temperature and chemical potential

The behaviour of the fermion charge Q localized on soliton at finite temperature T and chemical potential α is investigated in the one-dimensional continuum model of the linear diatomic polymer. It is shown that the depletion of the fermion charge takes place when T and α tend to its critical values. In the case of the spinless trans-polyacetylene model and N = 1 Gross-Neveu model the discontinuity of the value of Q at α_c is obtained whereas in the model φ⁴ with fermions the continuous transition to zero value of Q(α) occurs.