A convergent expansion about mean field theory: I. The expansion

We give a convergent expansion for nearly Gaussian quantum field theory in the multiphase region. The expansion combines (1) an expansion in phase boundaries, (2) a cluster expansion, and (3) a perturbation expansion to isolate dominant behavior. We study in detail the ground state of the $\text{P}$(φ)₂ = (λφ⁴ ? φ² ? μφ)₂ model, with ∥ μ ∥ ? λ² ? 1. The ground state is close to the classical free field, obtained by replacing $\text{P}$(φ) by the quadratic mean field polynomial $\text{P}$_c(φ), tangent to $\text{P}$ at a global minimum. Selecting one minimum gives a pure phase (ergodic ground state) satisfying the Wightman-Osterwalder-Schrader axioms with a positive mass. We also establish analyticity in λ for μ = 0 in the sector ∥ Im λ ∥ < ? Re λ ? 1, for ? ? 1.     

The critical behaviour of spontaneous magnetization in the antiferromagnetic NiO

The spontaneous magnetization of the sublattice vs temperature in the antiferromagnetic NiO was measured by the neutron diffraction method. Temperature changes of the Bragg peaks (111), (222), (333) and (444) with the wavelengths of neutrons $\text{λ}{}_{\mathrm{I}}\text{= 4.16}\text{A}\text{?}$, $\text{λ}{}_{\mathrm{II}}\text{= 2.08}\text{A}\text{?}$, $\text{λ}{}_{\mathrm{III}}\text{= 1.39}\text{A}\text{?}$ and $\text{λ}{}_{\mathrm{IV}}\text{= 1.04}\text{A}\text{?}$, respectively were simultaneously investigated by the neutron time-of-flight spectrometer. On the basis of these measurements, the transition temperature from the antiferromagnetic into the paramagnetic phase was determined, T_N = (523 ± 1)°K. The temperature function of the (111) magnetic peak intensity has been accepted to be I ～ (T_N?T)^2β. According to the present measurements the critical point exponent is 0.33 ± ^0.02_0.04.     

Electric and magnetic properties of the synthetic metal-copper subrodanide Cu(SCN)13

The temperature dependence of the resistance and magnetic susceptibility of the copper subrodanide Cu(SCN)_{$\text{1}\text{3}$} samples were measured at the magnetic field up to 7.3 kG and the temperature range 4.2–400 K. The resistance of the pressed pellet samples linearly increases with the temperature increasing and at 100–150 K the ?(T) line slope smoothly changes. The magnetic susceptibility at zero field linearly decreases with decreasing of the temperature, showing unusual exponential field dependence, which is rather strong at the room temperature and disappears at T → 0. It was concluded that a copper subrodanide is a synthetic metal.     

The influence of finite size on critical phenomena in Ni films

The depression of T_c for Ni films is found to be proportional to n^?λ where n is the number of atomic layers and λ = 1.33±0.13. This suggests that λ may equal $\text{1}\text{v}$ where v is the correlation length exponent.     

Multiple meron solutions of the classical Yang-Mills equation

We give a construction for multiple meron-antimeron solutions to the classical SU(2) Yang-Mills field equations. The corresponding charge density is $\text{Q(x) =}\text{1}\text{2}\text{∑ ± γ(x?x}{}_{\mathrm{i}}\text{)}$, with the x_i distinct points on a line. The problem is reduced to the solution of a scalar φ⁴ equation. We obtain a model with merons connected in pairs.     

On the theory of the low-temperature electrical resistivity of potassium

Expressing the residual resistivity ?₀ as a force-force correlation, a first-principles basis is afforded for the low temperature expansion of the electrical resistivity ? as

(I)$\text{? = ?}{}_0\text{[1 +}\text{λ1}\text{λ}\text{+ … ]}$

where λ = const T^-2 is the non-resistive mean free path arising from electron-electron scattering. λ¹ is found to reflect directly long-range correlations in the electronic motions via the off-diagonal behaviour of the local density of states at the Fermi energy.     

Phonon heating by hot electrons in n-InSb in quantizing magnetic fields

The effect of the phonon “narrow throat” was experimentally found in n-InSb in crossed electrical and quantizing magnetic fields at temperatures 1.6—4.2°K. The phenomenon of energy relaxation by hot electrons on phonons was detected with $\text{T}\text{S}\text{?}\text{h}\text{?}\text{λ}{}^{\mathrm{?1}}$ in the case of absence of a phonon thermal tank (S is sound velocity, λ is magnetic length, T is temperature). The value of a critical electric field (E_cr) on the S-type current-voltage characteristic (CVC) was measured as a function of temperature and the magnetic field.     

Effect of magnetic field on heat flow in a polyatomic gas in intermediate pressure range

The effect of a magnetic field, B, on heat flow in a gas in an intermediate pressure range has been studied. The ratio of the heat flow changes in the fields $\text{B}\text{⊥ ?T}$ and $\text{B}\text{6 ?T}$ was found to change nonmonotonically with pressure in N₂ and CO. With the decreasing pressure, a difference is observed between the dependence of heat flow on field orientation and the corresponding angular dependence in the limiting case Kn→0 ($\text{Kn}\text{=}\text{l}\text{/L}$, $\text{l}$ is the mean free path, L is the geometric size). An expression has been obtained for the heat flow in a magnetic field for Kn ? 0.1 from the solution of an integral kinetic equation. In particular, it has been shown that the special features of the Senftleben-Beenakker effect observed with the decreasing pressure arise not only due to spherically symmetric molecule-surface interaction, but also to nonspherical scattering on walls.     

Specific heats and phase transition in TMMC

The specific heats of the nearly one-dimensional antiferromagnet TMMC showed a sharp discontinuity in the temperature range ?(≡∥1?T/T_N∥) ≈ 2 × 10^-3 at T_N =0.835 ± 0.010 K. The remaining magnetic entropy below T_N is about 1% of its total for S = $\text{5}\text{2}$.     

Thermal and magnetic studies of the nearly one-dimensional antiferromagnetic system CsNiBr3

Magnetic susceptibility, specific heat and ¹³³Cs magnetic resonance measurements in a single crystal of CsNiBr₃ are reported. The data reveal two magnetic transitions separating the paramagnetic phase from the antiferromagnetic ground state. At the higher transition temperature T_N2 = (14.25 ± 0.05)K a net magnetic moment is observed only along the hexagonal c-axis, while only below the lower transition temperature T_N1 = (11.75 ± 0.05)K a perpendicular component of the magnetic moment appears also. Above T_N2 CsNiBr₃ can be described as a one-dimensional antiferromagnet with intrachain exchange interaction $\text{J}\text{k}{}_{\mathrm{B}}\text{= ?(17.0 ± 0.2)}\text{K}$ and single-ion anisotropy constant $\text{D}\text{k}{}_{\mathrm{B}}\text{? ?1.5}\text{K}$. Below T_N1, the data are consistent with the non-colinear triangular structure of the Ni²⁺ moments proposed previously for the isomorphic crystal CsNiCl₃. A reduced value of the zero-temperature susceptibility over the classical value is found and atrributed to the zero point deviations.     

Evaluation of activation energy by means of different trap spectroscopy techniques

Correlations are deduced for the asymmetry and the halfwidth of a signal peak which correspond to a discrete level using different “isothermal” trap spectroscopy techniques. Using only the temperature $\text{T}$ of the scan peak maximum and the halfwidth δ = T₂ ? T₁ the activation energy can then be determined: $\text{E =}\text{T}{}^2\text{/(δT}{}_{\mathrm{K}}\text{)}$, where T_K(=4500?6000 KeV^-1) is given numerically for certain frequently applied trap spectroscopy techniques. T_K is the result of a complete mathematical treatment of the kinetic equation.     

Courants critiques d'alliages supraconducteurs a concentration modulee spatialement II. — Effet de la temperature

The peak effect observed in the variation of the critical current as a function of the magnetic field H of periodically inhomogeneous films is observed only below a characteristic temperature T¹ given approximately by $\text{2ξ(T}{}^1\text{,}\text{C}\text{) = 2a}$ where 2a is the period of the modulation and C? the mean concentration. We describe the variation of the field values at peak J_c(H) as a function of temperature.     

Dynamics of the random field Ising model

Dynamics of the kinetic Ising model in the presence of static random fields is investigated using a self-consistent method. It is shown that if the interface fluctuations of the low temperature phase are small the system at low temperatures stays in a state without long range order. For this state the spin correlation function 〈S_q(t)S_?q(O)> averaged over all configurations of random fields decays exponentially in time with a single wavevector dependent relaxation time which is finite at the transition temperature T₀ and remains very long below T₀. In the mean field approximation the correlation time at the magnetic Bragg peak and at T₀ scales with the magnitude of the random field as τ∞h^?z_h with z_h = 1 for d = 2 and $\text{z}{}_{\mathrm{h}}\text{=}\text{4}\text{3}$ for d = 3, respectively.     

Dynamics of the infinite-range ising spin glass

The Glauber dynamics of an Ising spin glass with infinite-range interactions and additional static field, h, is investigated near the freezing temperature, T_f. We obtain critical slowing down at and below the de Almeida-Thouless instability line, h_c(T), to order (1?T/T_f)³ with algebraic decay of the spin correlations ～t^?ν, where $\text{ν=}\text{1}\text{2}$ at T_f and $\text{ν≤}\text{1}\text{2}$ for T<T_f.     

Necessary and sufficient conditions for the existence of a lagrangian. The case of quasi-linear field equations

Necessary and sufficient conditions for the existence of the Lagrangian associated with given field equations of motion are investigated. For the quasi-linear equations A_ab^μν(x^λ, φ^c, φ_?^c)φ_μν^b + B_a(x^μ, φ^b, φ_ν^b) = 0, the complete necessary and sufficient conditions are obtained, resorting to the formalism of an exterior derivative. It is emphasized that, to find expressions of these conditions, the anti-symmetric parts of the second derivatives of a Lagrangian, $\text{R}{}_{\mathrm{\mu \nu }}{}^{\mathrm{ab}}\text{= (}\text{?}{}^2\text{L}\text{?φ}{}_{\mathrm{\mu }}{}^{\mathrm{a}}\text{?φ}{}_{\mathrm{\nu }}{}^{\mathrm{b}}\text{?}\text{?}{}^2\text{L}\text{?φ}{}_{\mathrm{\nu }}{}^{\mathrm{a}}\text{?φ}{}_{\mathrm{\mu }}{}^{\mathrm{b}}\text{)/2}$, which disappear in the field equations, take an important role. The procedure to construct the Lagrandian associated with the field equations is also presented.     

Magnetic ordering in uranium monophosphide

The magnetic ordering in uranium monophosphide (UP) has been studied by neutron diffraction from a single crystal in a magnetic field. UP orders at T_N ? 122 ± 0.1 K with the type-I antiferromagnetic structure (+-+-), the ordering taking place in a first-order transition. At T₀ = 22.5 K the ordered magnetic moment jumps from 1.7 μ_B to 1.9 μ_B. With a magnetic field H = 25 kOe applied along the [11&#x0304;10] direction, it is found that UP has the collinear single-$\text{K}$ type-I structure above T₀ and undergoes a first-order transition to the planar double-$\text{K}$ type-I structure, accompanied by a “moment jump” due to the change in the moment direction from <001> to <110>.     

Pulsed magnetic field study of Fe2+ in some fluosilicates

Pulsed field experiments up to 450 kOe have been performed on FeSiF_6.6H₂O. We interpret the data: (i) in terms of spin hamiltonian constants: D = 12.3± 0.2 cm^-1 (E = 0.54cm^-1 being known from EPR data); (ii) in terms of axial-crystal-field parameters: $\text{δ}\text{λ}\text{=}\text{orbital trigonal splitting/spin-orbit coupling}\text{= 15 ± 2; λ = -100 ± 7cm}{}^{\mathrm{?1}}$. The magnetic axis is found to deviate from the cristallographie c axis by an angle 1° < θ < 2°. The adiabatic cooling obtained during the pulse is discussed.Similar experiments on Fe_0.15Zn_0.85SiF_6.6H₂O and Fe_0.30Zn_0.70SiF_6.6H₂O single crystals are reported; in both cases we measure $\text{D}\text{g}{}_{\mathrm{\parallel }}\text{= 6.0 ± 0.1cm}{}^{-1}$. Using EPR data, we obtain D = 14.3cm^-1, λ ～ ?75cm^-1, δ ～ 195cm^-1; using Mössbauer data, we obtain D = 15.3cm^-1, λ ～ ?88cm^-1, δ ～ 185cm^-1.     

On universality for area-preserving maps of the plane

We present detailed evidence that one-parameter families of area-preserving maps exhibit cascades of period doubling with universal geometric scaling in the parameter. We relate this behaviour to a fixed point equation of the form

$\text{Λ}{}^{\mathrm{?1}}\text{°Φ°Φ°Λ = Φ}$

and

$\text{det}\text{DΦ = 1}$

, Φ:$\text{R}$²→$\text{R}$². In particular we argue that the scaling transformation Λ:$\text{R}$²→$\text{R}$² is conjugate to the transformation Λ₀:(x, y)→(λx, μy), with λ² ≠ μ, and in fact λ² >μ. We present some numerical evidence that

$\text{δ = 8.721}$

…,

$\text{?}\text{1}\text{λ}\text{= 4.018}$

…,

$\text{1}\text{μ}\text{= 16.36}$

…, where δ is the asymptotic ratio of the differences of the parameter values corresponding to the successive periods 2^k described above.     

Critical behaviour of a uniaxial ferromagnet,ErCl3·6H2O with predominant dipolar interactions

The parallel magnetic susceptibility χ of a uniaxial ferromagnet ErCl₃·6H₂O has been measured between 0.3 and 4.2K and specially near T_c = 0.353 K. The predominant contribution to the Curie-Weiss temperature is due to the dipolar interactions. χ is proportional to ?^?γ with $\text{? =}\text{T}\text{T}{}_{\mathrm{c}}\text{?1}$ in the range 10^?3 < ? < 5 × 10^?2. The γ value, γ = 1.01 ±0.03 is consistent with the theoretical prediction for a uniaxial dipolar ferromagnet.