Renormalizable Models in Rank {d \geq 2} Tensorial Group Field Theory

Classes of renormalizable models in the Tensorial Group Field Theory framework are investigated. The rank d tensor fields are defined over d copies of a group manifold \({G_D=U(1)^D}\) or \({G_D= SU(2)^D}\) with no symmetry and no gauge invariance assumed on the fields. In particular, we explore the space of renormalizable models endowed with a kinetic term corresponding to a sum of momenta of the form \({p^{2a}, a\in (0,1]}\) . This study is tailored for models equipped with Laplacian dynamics on G _D (case a = 1) but also for more exotic nonlocal models in quantum topology (case 0 < a < 1). A generic model can be written \({(_{\dim G_D}\Phi^{k}_{d}, a)}\) , where k is the maximal valence of its interactions. Using a multi-scale analysis for the generic situation, we identify several classes of renormalizable actions, including matrix model actions. In this specific instance, we find a tower of renormalizable matrix models parametrized by \({k \geq 4}\) . In a second part of this work, we study the UV behavior of the models up to maximal valence of interaction k = 6. All rank \({d \geq 3}\) tensor models proved renormalizable are asymptotically free in the UV. All matrix models with k = 4 have a vanishing β-function at one-loop and, very likely, reproduce the same feature of the Grosse–Wulkenhaar model (Commun Math Phys 256:305, 2005).     

Influential Factors of Internal Magnetic Field Gradient in Reservoir Rock and Its Effects on NMR Response

Nuclear magnetic resonance (NMR) plays a significant role in porous media analysis and petroleum exploration, but its response is significantly influenced by the internal magnetic field gradient in fluid saturated porous medium, which obviously limits the accuracy of rock core analysis and logging interpretation. The influential factors of the internal magnetic field gradient in formation and its influences on NMR response are studied in this paper, based on NMR mechanism through one- and two-dimensional core NMR experiments. The results indicate that the internal magnetic field gradient is positively correlated with the static magnetic field strength and the magnetic susceptibility difference between pore fluid and solid grains, while it presents negative correlation with pore radius. The internal magnetic field gradient produces an additional diffusion relaxation in hydrogen relaxation system and accelerates the attenuation of magnetization vector. As a result, T₂ spectrum shifts to the left and NMR porosity and diffusion coefficient of the fluid could be inaccurate. This research sets a foundation for the NMR porosity correction and fluid distribution on T₂-G maps based on the internal magnetic field gradient correction.     

Structural characterization,magnetic properties and magnetocaloric effects of La0.75Sr0.25Mn1–x Cr x O3 (x = 0.15, 0.20, and 0.25)

The effect of Cr doping on the structural, magnetic and magnetocaloric properties of perovskite manganites La_0.75Sr_0.25Mn_1–x Cr _x O₃ (x = 0.15, 0.20, and 0.25) has been investigated. Crystalline structure and magnetic properties are investigated by using X-ray powder diffraction and magnetization measurements, respectively. All samples show a single phase and are found to crystallize in the distorted rhombohedral system with \( R\overline{3} \,c \) space group. A monotonous change of Curie temperature (T _C), from 314 to 253 K, is observed when content doping increases. Substantial magnetic entropy change reaching 4.20 J/kg K is revealed. Relative cooling power was estimated as well. It was found to reach 289, 323, and 386 J/kg for x = 0.15, 0.20, and 0.25, respectively. Field dependence of the magnetic entropy change showing the power law dependence \( \Delta S_{\rm M} \propto \,\,\left( {\mu_{ 0} \rm H} \right)^{n} \) is also analyzed and discussed.     

Efimov Spectrum in Bosonic Systems with Increasing Number of Particles

It is well-known that three-boson systems show the Efimov effect when the two-body scattering length a is large with respect to the range of the two-body interaction. This effect is a manifestation of a discrete scaling invariance (DSI). In this work we study DSI in the N-body system by analysing the spectrum of N identical bosons obtained with a pairwise gaussian interaction close to the unitary limit. We consider different universal ratios such as \({E_N^0/E_3^0}\) and \({E_N^1/E_N^0}\) , with \({E_N^i}\) being the energy of the ground (i = 0) and first-excited (i = 1) state of the system, for \({N \leq16}\) . We discuss the extension of the Efimov radial law, derived by Efimov for N = 3, to general N.     

Determination of the positions of impurity centers in a dislocation core in a NaCl crystal from magnetoplasticity spectra

The spectra of the mean free paths l(ν) of edge dislocations have been studied in NaCl crystals exposed in the electron paramagnetic resonance scheme to the crossed magnetic fields: the Earth’s field (50 μT) and the pump field (2.5 μT, 5–440 kHz). The spectra have been measured for a series of angles θ = 0°–5° of rotation of the sample around its edge [100] with respect to the Earth’s field. The fine structure of the spectra contains a series of peaks whose resonance frequencies are described by the empirical expression v _i ^± = Asin(θ ± Δθ _i ) ≈ A(θ ± Δθ _i ). The parameters Δθ _i are independent of the angle θ within the experimental errors. Within the model of “frozen” magnetic moments associated with impurity center Ca⁺-Cl⁰, the angles Δθ _i characterize the deviation of the axis of the center from the 〈100〉 direction in the core of a dislocation. These angles can be expressed in terms of the spectra obtained: Δθ _i = (? _i ⁺ ? v _i ^? )/2A. The computer simulation of the edge dislocation core provides the set of the angles Δθ _i close to the measured values. The spin-lattice relaxation time of the center on dislocation has been estimated from the low-frequency edge of the spectrum l(ν) as τ _{s ? l} ～ 10^?4 s.     

Diffusion Effects on the Breakdown of a Linear Amplifier Model Driven by the Square of a Gaussian Field

We investigate solutions to the equation ? _t ?? $\mathcal{D}$ Δ?=λS ²?, where S(x, t) is a Gaussian stochastic field with covariance C(x?x′, t, t′), and x∈ $\mathbb{R}$ ^d . It is shown that the coupling λ _cN (t) at which the N-th moment <? ^N (x, t)> diverges at time t, is always less or equal for $\mathcal{D}$ >0 than for $\mathcal{D}$ =0. Equality holds under some reasonable assumptions on C and, in this case, λ _cN (t)=Nλ _c (t) where λ _c (t) is the value of λ at which <exp[λ ∫ ^t ₀ S ²(0, s) ds]> diverges. The $\mathcal{D}$ =0 case is solved for a class of S. The dependence of λ _cN (t) on d is analyzed. Similar behavior is conjectured when diffusion is replaced by diffraction, $\mathcal{D}$ →i $\mathcal{D}$ , the case of interest for backscattering instabilities in laser-plasma interaction.     

Negative magnetoresistance and hall coefficient of a two-dimensional disordered system

Localization corrections to the longitudinal (δρ) and Hall (δρ_H) resistivities of a two-dimensional disordered system are calculated in all ranges of classical magnetic fields, up to the values at which the mean free path of charge carriers l is less than or of the order of the cyclotron radius R _c. It is shown that the physical reason for the departure of the l dependence of these resistivities from the logarithmic law ∝ ln(l _B /l)) (l _B is the magnetic length) at is the nonlocal process of diffusion in the Cooper channel, rather than the transition to a quasi-ballistic regime. Analytical expressions are obtained that allow one to analyze the interference effect in δρ and δρ_H in quantizing magnetic fields , including the quantum limit. Contrary to popular opinion, the localization corrections to ρ_H are shown to be nonzero. They have a sign opposite to that of the charge carriers and lead to a decrease in the magnitude of the Hall resistivity. Their field dependence has the same features and their relative magnitude is of the same order as in the case of the longitudinal resistivity. The quantum corrections to the Hall resistivity are due to the Larmor precession of the closed paths that electrons follow in the process of their multiple scattering by randomly distributed impurities.     

Magnetic moment of proton halo nucleus 28 P

The magnetic moment of ²⁸P (I _π = 3^?+?, T_1/2 = 270.3 ms) in the ground state has been measured by the $\upbeta $ -nuclear magnetic resonance method for the first time. The measured magnetic moment of $\vert \upmu (^{28}$ P)∣ = 0.309(9)  $\upmu _{{\rm N}}$ is well reproduced by the shell model value of +0.306  $\upmu _{{\rm N} }$ . The shell model calculation also yields a proton density distribution with a long tail. The present results provide a strong confirmation of the configuration of the 2s _1/2 proton which should lead to the proton halo.     

Probing new physics through B→Kl + l − decays in R-parity violating minimal supersymmetric standard model

We study the decay rate of the process B→Kl ⁺ l ^? (l=e,μ) and some of its other related observables, like the forward–backward asymmetry (A _FB), polarization asymmetry (PA), double branching ratio and CP asymmetry (A _CP) in the R-parity violating Minimal Supersymmetric Standard Model ( $\not \!{R}_{p}$ MSSM). We have performed an error analysis of the differential branching fraction, A _FB and CP asymmetry. The analysis shows that theoretical results based on $\not \!{R}_{p}$ MSSM as an additional effect are compatible with the standard model. A _FB is found to be zero, in agreement with SM. The average A _CP is not only found to be significant in comparison with SM, but it is also compatible with the measured value within errors.     

Resonant dislocation motion in NaCl crystals in the EPR scheme in the Earth’s magnetic field with pulsed pumping

Resonant dislocation motions in NaCl(Ca) crystals under the simultaneous action of the Earth’s magnetic field B _Earth (～66 μT) and a pulsed pump field $\tilde B$ of sufficient amplitude $\tilde B_m $ and certain duration τ have been detected and studied. The measured dislocation path peaks l(τ) have a maximum at τ = τ _r ≈ 0.53 μs. The resonance criterion has been found to be the ordinary EPR condition in which the g-factor is close to 2 and the optimum inverse pulse duration τ _r ^?1 is used instead of the harmonic pump field frequency ν _r . The largest peak l(τ) height is reached at mutually orthogonal dislocation (L) and magnetic field (B _Earth and $\tilde B$ ) orientations. Pulsed field rotation to the position $\tilde B$ ‖ B _Earth significantly decreases but does not “kill” the effect. For dislocations parallel to the Earth’s field (L ‖ B _Earth), the resonance almost disappears even at $\tilde B$ ⊥ B _Earth. In the optimum geometry of experiments, as the pump field amplitude $\tilde B_m $ decreases from 17.6 to 10 μT, the path peak height l _r = l(τ _r ) decreases only by 7.5%, remaining at the level of l _r ～ 10² μm, and at a $\tilde B_m $ further fall-off to 4 μT, it rapidly decreases to background values. In this case, the relative density of mobile dislocations similarly decreases from ～90 to 40%. Possible physical mechanisms of the observed effect have been discussed.     

Heat Conduction and Entropy Production in Anharmonic Crystals with Self-Consistent Stochastic Reservoirs

We investigate a class of anharmonic crystals in d dimensions, d≥1, coupled to both external and internal heat baths of the Ornstein-Uhlenbeck type. The external heat baths, applied at the boundaries in the 1-direction, are at specified, unequal, temperatures T _l and T _r . The temperatures of the internal baths are determined in a self-consistent way by the requirement that there be no net energy exchange with the system in the non-equilibrium stationary state (NESS). We prove the existence of such a stationary self-consistent profile of temperatures for a finite system and show that it minimizes the entropy production to leading order in (T _l ?T _r ). In the NESS the heat conductivity κ is defined as the heat flux per unit area divided by the length of the system and (T _l ?T _r ). In the limit when the temperatures of the external reservoirs go to the same temperature T, κ(T) is given by the Green-Kubo formula, evaluated in an equilibrium system coupled to reservoirs all having the temperature T. This κ(T) remains bounded as the size of the system goes to infinity. We also show that the corresponding infinite system Green-Kubo formula yields a finite result. Stronger results are obtained under the assumption that the self-consistent profile remains bounded.     

Magnetic phase transitions and iron valence in the double perovskite Sr 2 FeOsO 6

The insulating and antiferromagnetic double perovskite Sr₂FeOsO₆ has been studied by ⁵⁷Fe Mössbauer spectroscopy between 5 and 295 K. The iron atoms are essentially in the Fe^3?+? high spin $( {t_{2\mathrm{g}}{^3} e_\mathrm{g}{^2} } )$ and thus the osmium atoms in the Os $^{5+} ( {t_{2\mathrm{g}}{^3} } )$ state. Two magnetic phase transitions, which according to neutron diffraction studies occur below T _N?= 140 K and T ₂?= 67 K, give rise to magnetic hyperfine patterns, which differ considerably in the hyperfine fields and thus, in the corresponding ordered magnetic moments. The evolution of hyperfine field distributions, average values of the hyperfine fields, and magnetic moments with temperature suggests that the magnetic state formed below T _N is strongly frustrated. The frustration is released by a magneto-structural transition which below T ₂ leads to a different spin sequence along the c-direction of the tetragonal crystal structure.     

Magnetic-impurity states of electron in two-dimensional semiconductor structures

Electron states on an attractive center of small-radius r _c ? l (l = $\sqrt {\frac{{c\hbar }}{{eH}}} $ is the magnetic length) located in a two-dimensional structure are investigated in a uniform magnetic field H applied perpendicularly to the structure surface. The spectrum of magnetic-impurity (MI) particle states with an arbitrary moment projection on the direction H for Landau bands 0 ≤ N < l ²/r _c ² is derived in the approximation that mixing of Landau levels is weak. The dependence of the electron energy states on magnetic field, the layer thickness, and the impurity position are studied. It is shown that dimension lowering leads to a qualitatively different spectrum of MI states compared to the three-dimensional case [1]. A comparison of the obtained binding energy of the D ^? center with experimental data is performed.     

Mössbauer study of magnetism in FeII − III (oxy-)hydroxycarbonate green rusts; ferrimagnetism of FeII − III hydroxycarbonate

Fe^II???III hydroxycarbonate Fe $^{\rm II}_{4}$ Fe $^{\rm III}_{2}$ (OH)₁₂CO₃, green rust GR(CO $_{3}^{2-})$ , reveals a ferrimagnetic behaviour. Moments that lie within two-dimensional cation layers are parallel for same species and antiparallel between Fe^II and Fe^III. Respective ordering temperatures are 5.2 and 7 K. A sextet with distribution from 350 to 580 kOe for Fe^III and an octet reflecting a mixture of states with field of 130 kOe and quadrupole splitting of ?3.0 mm s^???1 for Fe^II are observed at 1.4 K. Ferric oxyhydroxycarbonate Fe $^{\rm III}_{6}$ O₁₂H₈CO₃ is ferromagnetic and displays at 4 K a sextet with field between 400 and 500 kOe (maximum at 480 kOe) and transition at 80 K. GR(CO $_{3}^{2-})$ deprotonation gives magnetic domains with compositions at x?=?1/3, 2/3 and 1 due to long range order.     

Determination of theg j -factor in the72 P 3/2-state of133Cs by optical double resonance in a strong magnetic field

The hfs in the 7² P _3/2-state of¹³³Cs has been investigated by optical double resonance in a strong magnetic field. From the positions of the magnetic dipole transitions Δm _j =± 1, Δm _i =0 the magnetic hfs coupling con slanta (7² P _3/2)=16.591(25) MHz and theg _j -factorg _j (7² P _3/2)=1.33410(15) could be derived. Contrarily to recent measurements,g _j agrees well with the value calculated from the Lande formula.     

Construction of kernels of the nonlinear collision integral in the Boltzmann equation using laplace transformation

It is shown that the relation between kernels L _l (v, v ₁) of the linear collision integral and kernels G _l,0 ^l (v, v ₁, v ₂) of the nonlinear collision integral can be reduced to the Laplace transformation. Analytic expressions for nonlinear kernels G _0,0 ⁺⁰ (v, v ₁, v ₂) and G _1,0 ⁺¹ (v, v ₁, v ₂) are determined for hard spheres and pseudo-Maxwellian molecules.     

Evolution of structural,magnetic and magnetocaloric properties in Sn-doped manganites La0.57Nd0.1Sr0.33Mn1−x Sn x O3 (x = 0.05–0.3)

Structural and magnetic properties of manganites series La_0.57Nd_0.1Sr_0.33Mn_1?x Sn _x O₃ with (0.05 ≤ x ≤ 0.30) have been investigated, and the critical exponents and magnetocaloric effect are studied around the room temperature, to shed light on Sn substitution influence. A solid-state reaction method was used in the preparation. A structural study using Rietveld refinement of XRD patterns indicates rhombohedral structure with R \( \overline{3} \) c space group for (0.05 ≤ x ≤ 0.20) and shows the existence of a secondary phase attributed to the neodymium tin oxide (Nd₂Sn₂O₇) pyrochlore for x = 0.3. The variation of the magnetization (M) vs. temperature (T), under an applied magnetic field of 0.05 T, reveals a ferromagnetic–paramagnetic transition at the Curie temperature T _C. In addition, it was discovered that increasing the tin content leads to a reduction in magnetization and a lowering of T _C from 282 K (x = 0.05) to 158 K (x = 0.20) with increasing Sn substitution. The samples exhibit the characteristics of spin/cluster-glass state which is evident from (zero-field-cooled and field-cooled) magnetization vs. temperature curves. Indeed, the thermal evolution of magnetization in the ferromagnetic phase at low temperature varies as T ^3/2, in accordance with Bloch’s law. The spin-stiffness constant D obtained from the Bloch constant was determined. A large magnetocaloric effect has been observed in both samples (x = 0.05 and x = 0.10): the maximum entropy change, \( \left| {\varDelta S_{\text{M} }^{\text{peak}} } \right| \) , reaches the highest value of 3.22 J/kg K under a magnetic field change of 5 T with a RCP value of 56 J/kg for x = 0.10 composition. This opens an interesting opportunity to this compound to compete with materials which work as magnetic refrigerants near room temperature. Besides, we show that the samples follow the conventional behavior of a second-order ferromagnetic transition. This was possible by investigating the critical behavior at the transition region by adopting the modified Arrott plot method. The values of the critical exponents (β, γ, δ and n) are determined and they are between those predicted by the three-dimensional Heisenberg model.     

Improved electrical properties of La2/3Ba1/3MnO3:Ag0.04 thin films by thermal annealing

La_2/3Ba_1/3MnO₃:Ag_0.04 (LBMO:Ag_0.04) thin films were prepared on single crystalline (001)-orientated LaAlO₃ substrates by pulsed laser deposition technique. Thermal annealing with temperatures of 780, 800 and 820 °C has been investigated to improve electrical properties of the films. All the samples are shown along the (00l) orientation in rhombohedral structure with \( R\overline{3} c \) space group. With thermal annealing temperature increasing, insulator–metal transition temperature (T _p) and resistivity at T _p ( \( \rho_{{T_{\text{p}} }} \) ) of the epilayer reach optimal value of 288 K and 0.03 Ω·cm, respectively. The electrical properties improvement of the LBMO:Ag_0.04 films is due to an improved film crystallization, oxygen balance and photon scattering suppression. The fitting curves show that the region of ferro-magnetic metallic (FM, T < T _p) is fitted with grain/domain boundary, electron–electron and magnon scattering mechanism, as well as the region of para-magnetic insulating (PI, T > T _p) is fitted with adiabatic small polaron hopping mechanism.     

The Influence of the Magnetic Impurity Content on the Pore Size Distribution Determination via the DDIF Technique

The pore size distribution of porous media can be determined in a completely non-invasive manner using a new nuclear magnetic resonance (NMR) technique which monitors the magnetization decay due to diffusion in internal fields (DDIF). However, using of the DDIF technique is restricted to the low-phase encoding limit when only the relaxation mode and the first-order diffusion mode are excited. In the present work the fulfillment of such a limit is verified for a progressive increase of the magnetic impurity content of the porous media. If the higher order diffusion modes are excited they lead both to a stronger attenuation of the echo signal and to the appearance of ripples in the DDIF spectra which cannot be related to a pore size distribution. The samples used in this study are porous ceramics prepared using the replication technique and the magnetic impurity is iron (III) oxide which is introduced in an increasing concentration inside the porous matrix. All NMR experiments were done on water filling such porous ceramics using a low-field instrument operating at a proton resonance frequency of 20 MHz. The average pore dimension obtained with the DDIF technique in the weak encoding limit indicates a satisfactory agreement with that observed in optical microscopy images.