Four-parametric regular black hole solution

We present a regular class of exact black hole solutions of the Einstein equations coupled with a nonlinear electrodynamics source. For weak fields the nonlinear electrodynamics becomes the Maxwell theory, and asymptotically the solutions behave as the Reissner–Nordström one. The class is endowed with four parameters, which can be thought of as the mass m, charge q, and a sort of dipole and quadrupole moments and , respectively. For 3, 4, and |q|2s _c m the corresponding solutions are regular charged black holes. For = 3, they also satisfy the weak energy condition. For = = 0 we recover the Reissner–Nordström singular solution and for = 3, = 4 the family includes a previous regular black hole reported by the authors.     

Phases of the number-theoretic spin chain

We present numerical and analytical evidence for a first-order phase transition of the ferromagnetic spin chain with partition functionZ()=(–1)/() at the inverse temperature _cr=2.     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.     

Analyticity properties of the surface free energy of the Ising model

For an Ising ferromagnet with nearest-neighbour interactions of strengthK and surface magnetic fieldh, the surface free energy in the presence of a positively (or negatively) magnetized zero-field bulk phase is shown to be analytic inh for Reh<K–/, where =2.96 ... and is the inverse temperature. This puts the lower boundK–/ on the values ofh at which wetting and layering transitions can take place.     

The influence of tensile stress on grain and cell boundary precipitation in supersaturated Al-Zn alloys during creep

The results are presented of the optical microscopic and X-ray diffraction study of the stress-induced nucleation and growth of (Zn) precipitates at grain and cell boundaries (GB's and CB's) during uniaxial creep at 200 °C of supersaturated AlZn20 and AlZn30 alloys. The rate of precipitation is increased mainly owing to the modifying effect of tensile stress on diffusion processes in alloy samples during their anneal. The diffusion of Zn atoms toward GB's and CB's from adjacent regions of grains is accompanied during creep by diffusive flux of Zn along boundaries parallel or nearly parallel to the tensile creep axis toward boundaries with near to normal orientation to that axis. Enhanced precipitation of results then preferentially at the latter and is supressed at the former boundaries where even the dissolution of preexisting has been found during a later application of tensile stress. The stress-induced precipitation of at GB's gradually ceases with prolonged creep exposures due to the lengthening of duffusion paths of Zn atoms from grain interior to GB's.Dissolution of lamellae by their regress toward GB's and CB's is assisted with the stress-induced diffusion of Zn along epitaxial / lamellar interfaces. Copious precipitation of at the parts of GB's and/or CB's with near to normal orientation to the creep axis is then observed on account of Zn from dissolved lamellae. Creep strain also leads to the fragmentation of lamellae and thus also to breaking down of the paths for diffusion of Zn along / interfaces. Spheroidization of fragmented parts of lamellae is then observed. Spheroids of remain embedded within the former lamellar regions.Large creep strains and high strain rates observed on fine-grained alloy samples may be associated with an enhanced viscous GB sliding due to the stress-dependent flow of Zn along GB's and/or CB's.     

The energy-momentum gravitational pseudotensor and Kerr-Schild metrics

It is shown that the Landau-Lifshitz pseudotensor vanishes for any Kerr-Schild metricg =n + 2Hl l satisfying the conditionS l =0. Some solutions verifying this condition are indicated.     

Correlated majority model

We extend the bichromatic majority model by including (one-dimensional isotropic) correlations and numerically discuss, through Monte Carlo simulations, the simple, 1/3, and 2/3 majority rules. We calculate, as functions of the concentration and correlation degree, the mean finite cluster size, and the order parameterm as well as their respective critical exponents and. We find1 regardless of the correlation degree or the type of majority. Also, a supplementary divergence of is observed at the>0 borderline.     

Deviation of Upper Bounds of Critical Temperature of Two-Dimensional O(N) Spin Models

Critical temperature of the classical O(N) spin model in two dimensions is investigated. We show that no phase transition exists in the system if the inverse temperature is less than _c=_c(N), where _c(N) is a constant such that _c(N) > const. N log N.     

Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

Statistically periodic processes and toeplitz(α by β) matrices

If each element in a Toeplitz matrix is replaced by an by matrix and the original constraints preserved, the result is a doubly infinite matrix with periodic structure called a toeplitz_{( by)} matrix. Such matrices are a basic tool for describing, generating, estimating, filtering, synchronizing, and analyzing information-theoretic functions for statistically periodic processes.     

Vacuum Einstein spaces with axial symmetry

Four classes of solutions are found to the equations R=–2_{; ;} and g _;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations R_ij=0 in a vacuum for the metric . The metric ds² assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.     

The low-temperature phase of Kac-Ising models

We analyze the low-temperature phase of ferromagnetic Kax-Ising models in dimensionsd2. We show that if the range of interactions is ^–1, then two disjoint translation-invariant Gibbs states exist if the inverse temperature satisfies –1^N, where =d(1–)/(2d+2)(d+1), for any >0. The proof involves the blocking procedure usual for Kac models and also a contour representation for the resulting long-range (almost) continuous-spin system which is suitable for the use of a variant of the Peierls argument.     

Zero value of the Schwarzschild mass for an asymptotically Euclidian system of gravitational waves

A class of the asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions: _k (-gg ^0k )=0 and _ik ⁰ _0g ^ik - _ik ^k _0g ⁰ⁱ =0. In aT-orthogonal metricgs ²=g ₀₀ dt ² -g dx dx these conditions take a simple form: ₀(detg )=0 and (₀ g )(₀ g )=0.     

Low-temperature phase transitions in GdS,GdSe and GdTe

In the Gd monochalcogenides up to three different structural distortions have been detected in the magnetically ordered regime. Our experiments indicate that all three phases show type II antiferromagnetic order but with different orientations of the magnetic moments: A truly trigonal phase withm _k k=[1/2, 1/2, 1/2], a monoclinic phase withabc, =/2+, and the spins oriented along [110], and a pseudo-rhombohedrally compressed monoclinic phase with the spins in the (111) planes. The spin flips can be accounted for by a model including anisotropic exchange interactions.     

Transfer Matrix Spectrum and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We obtain new properties of general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high-temperature region (1). Each model is characterized by a single-site a priori spin distribution, taken to be even. We state our results in terms of the parameter =s ⁴–3s ²², where s ^k denotes the kth moment of the a priori distribution. Associated with the model is a lattice quantum field theory which is known to contain particles. We show that for >0, small, there exists a bound state with mass below the two-particle threshold. The existence of the bound state has implications for the decay of correlations, i.e., the 4-point functions decay at a slower rate than twice that of the 2-point function. These results are obtained using a lattice version of the Bethe–Salpeter equation. The existence results generalize to N-component models with rotationally invariant a priori spin distributions.     

Double quantum transitions in paramagnetic resonance

The theory of double quantum transitions of the M=±2 type, with regard to inhomogeneously broadened spin systems is studied in this paper with the approximation ²T₂T₃ 1. We suppose that the inhomogeneous broadening is formed by an inhomogeneous crystal field. The obtained results describe the magnitude of absorption as a function of the h.f. power and also describe the shape of the absorption curve. It is demonstrated that in inhomogeneously broadened spin systems the absorption curve of double quantum transitions has the form of the difference of two different Lorentz's curves and that at the saturation ( ²T₂T₁ 1) the absorption increases with the cube of the h.f. field intensity. The shape of the curves is expressed by means of phenomenological relaxation constants of the system.

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M=±2 ²T₂T₃ 1. , - . . , ( ²T₂T₁ 1) . .

     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Glueball spectroscopy in strongly coupled lattice gauge theories

We study the mass spectrum up to –7 (1–) log of pure three-dimensional lattice gauge theories with action (g _P) for real irreducible and small . Besides the lowest excitationm ₀–4log, we find two nearly degenerate excited statesm ₁,m ₂ withm _i–6log (i=1, 2) and (m ₁–m ₂) at leastO().Work partially supported by CNPq (Brasil)     

Combining Multifractal Additive and Multiplicative Chaos

The purpose of this article is the study of the new class of multifractal measures, which combines additive and multiplicative chaos, defined bywhere is any positive Borel measure on [0,1] and b is an integer 2. The singularities analysis of the measures _, involves new results on the mass distribution of when describes large classes of multifractal measures. These results generalize ubiquity theorems associated with the Lebesgue measure.Under suitable assumptions on , the multifractal spectrum of _, is linear on [0,h_, ] for some critical value h_, . Then is strictly concave on the right of h_, , and on this part it is deduced from the multifractal spectrum of by an affine transformation. This untypical shape is the result of the combination between Dirac masses and atomless multifractal measures. These measures satisfy multifractal formalisms. They open interesting perspectives in modeling discontinuous phenomena.     

Magnetic studies on synthetic phosphoferrite Fe 3 2+ (H2O)3(PO4)2

Synthetic crystals of phosphoferrite were studied by Mössbauer spectroscopy for temperatures ranging from 4.2 to 17.5 K. The analysis of the behaviour of the hyperfine fields for the two unequivalent sites near the Néel temperature (17.4 K) allowed the determination of the critical exponent for each site as ₁=0.171 and ₂=0.314.