On the magnetic properties of transition metal substituted MnAs

The properties of Mn_1?tT_t As phases (T: V, Cr, Fe or Co; 0<t$\text{\$}\text{?}$= 0.10) are studied in external magnetic fields up to 250 kOe, and temperatures between 80 and 400 K. The results are presented and discussed in terms of phase diagrams comprising concentration, temperature, and magnetic field axes.     

On a least upper bound Tc of superconductors with paramagnetic impurities

We have obtained a least upper bound, $\text{k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{c}}\text{? c(μ}{}^1\text{, t)A}$, on the critical temperature T_c of an isotropic superconductor with paramagnetic impurities described by the scattering matrix t for fixed values of μ¹. We have also obtained the corresponding optimal spectrum $\text{α}{}^2\text{F(m) = Aδ[ω?d(μ}{}^1\text{, A]}$. The numerical results for the functions $\text{c(μ}{}^1\text{, t)}\text{and}\text{d(μ}{}^1\text{, t)}$ are presented for $\text{α}{}^1\text{= 0.1}$ and 0.16 in the form of universal curves representing $\text{c(μ}{}^1\text{, t)}\text{and}\text{d(μ}{}^1\text{, t)}$ as functions of the reduced impurity concentration $\text{t}\text{= t/A}$. We have also established an upper limit to the reduced critical concentration $\text{t}{}_{\mathrm{crit}}$ for an arbitrary shape of α²F(ω)1.     

Magnetic Phase transitions and hysteresis in FeCl2 · 2H2O

The magnetic phase diagram of FeCl₂ · 2H₂O has been determined by means of single crystal neutron diffraction experiments. Isothermal and isobaric measurements reveal the existence of first order and second order phase transitions separated by tricritical points at $\text{t}{}_1{}^1\text{= 0.5, h}{}_1{}^1\text{= 0.91}\text{and}\text{t}{}_2{}^1\text{= 0.39, h}{}_2{}^1\text{= 0.99}$. Considerable hysteresis effects were observed at the antiferro—ferrimagnetic phase boundary at temperatures t < 0.33.     

Equilibrium of three liquid phases and approach to the tricritical point in benzene-ethanol-water-ammonium sulfate mixtures

We have determined the region of coexistence of three liquid phases in the system C₆H₆-EtOH-H₂O-(NH₄)₂SO₄ at 21°, 45°, 48° and 48.6°C, and have located the tricritical point. The temperature and composition at the tricritical point are T_t = 48.9°C and mass fractions x_salt = 0.0175, x_water = 0.351, x_ethanol = 0.450, x_benzene = 0.181. This composition is inferred to lie outside the three-phase region at 21° and 45°, in agreement with the phenomenological theory of Griffiths. The locus of the three liquid phases in the isothermal composition tetrahedron has the parabolic, inflected (cubic), and cusped aspects predicted by the theory. For the three exponents β₁, β₂, and β₃ associated with the vanishing of the three characteristic dimensions of the coexistence region, we find β₁ = 0.4, β₂ = 1.0, β₃ = 1.5, compared to the theoretical $\text{β}{}_1\text{=}\text{1}\text{2}\text{, β}{}_2\text{= 1, β}{}_3\text{=}\text{3}\text{2}$. We verify that the algebraic degree 1/β′ of the coexistence curve near the two critical end points exceeds its classical value of 2.     

Measurements of elastic scattering in alpha-alpha and alpha-proton collisions at the CERN intersecting storage rings

We measured the elastic scattering of $\text{αα}\text{at}\text{s}\text{= 126}\text{GeV}$ and of αp at $\text{s}\text{= 89}\text{GeV}$. For αα, the differential cross section dσ/dt has a diffractive pattern minima at |t| = 0.10 and 0.38 GeV². At small |t| = 0.05?0.07 GeV², this cross section behaves like exp[(100 ± 10) t]. Extrapolating a fit to the data to the optical point, we obtained for the total cross section α_tot(αα) = 250 ± 50 mb and an integrated elastic cross section σ_e1(αα) = 45 ± mb. Another method of estimating σ_tot(αα), based on measuring the interaction rate, yielded 295 ± 40 mb. For αp, dσ/dt has aminimum at |t| = 0.20 GeV², and for 0.05 < |t| < 0.18 GeV² behaves like exp[(41 ± 2) t]. Extrapolating this slope to |t| = 0, we found σ_tot(αp) = 130 ± 20 and σ_e1(αp) = 20 ± 4mb. Results on pp elastic scattering at $\text{s}\text{= 63}\text{GeV}$ agree with previous ISR experiments.     

Supersymmetry and the division algebras

We show how spinors in space-times of dimension D = t + s, where t is the time dimension, are associated for s - t = 1, 2, 4, 8 (and if t = 0, 1, 2) with the number systems (division algebras), $\text{|R, C, H, O}$. For t = 1 and s - t = 1, 2, 4 this association is “realized” by the sequence of Lorentz groups S1(2,$\text{|R}$), S1(2;$\text{|C}$), S1(2;$\text{|H}$) for D = 3, 4, 6 respectively. We discuss how octonions may be related to D = 10. For D = 6 we give details of S1(2; $\text{|H}$) spinors and construct supersymmetric models with them. These results explain various “empirical” observations in the literature relating quaternions and supersymmetry.     

Scaling function for order-parameter correlations in expansion to order 1/n: I. Short-range interactions

The order-parameter correlation function $\text{G}\text{?}\text{(}\text{q}\text{, ξ}{}_1\text{)}$ is calculated in the critical region of momentum space $\text{q}$ in terms of a second-moment correlation length ξ₁ by means of perturbation expansion to order 1/n, for an n-vector system with short-range interactions, in zero field above T_c, for 2 < d < 4. The scaling function of the $\text{q}$ dependence is obtained in closed form with a precisely identified cutoff-dependent factor which is the amplitude of the correlation-length dependence of the susceptibility. Both the exponents and the coefficients of the expansion for fixed q as t = (T?T_c)/T_c → 0 are given explicitly and the former are shown to be in accordance with the operator product expansion. The coefficients of order 1/n in the terms associated with a t^k(1?α) dependence of the energy density, for integer k ≥ 1, are expected to be explicitly cutoff-dependent and this is verified by the detailed calculations for k = 1. The behaviour for fixed t and q → 0 is shown to be markedly different from the Ornstein-Zernike approximation. Detailed comparison is provided with the scaling function of the t dependence of the correlations appearing in parallel work.     

Specific heat studies of randomly diluted magnets evidence for fractal properties of the infinite percolation cluster

We present specific heat data on the system Fe_pZn_1-pL₆(ClO₄)₂, which is an experimental realization of the sc, $\text{S =}\text{1}\text{2}$, diluted Ising antiferromagnet. Here L = C₅H₅NO. The results are compared with earlier data on the diluted sc, $\text{S =}\text{1}\text{2}$, XY antiferromagnet Co_pZn_1-pL₆(Cl)₄)₂ and the diluted bcc, $\text{S =}\text{1}\text{2}$, Ising antiferromagnet Co_pZn_1-pCs₃Cl₅. The specific heat behaviour of the diluted Ising systems is found to be completely different from that of the diluted XY magnet, for which very strong short-range order effects have been observed. An explanation is given in terms of the fractal properties of the infinite percolation cluster in the temperature range above T_c(p). It is shown that there exists a strong analogy between the specific heat behaviour of a diluted magnet and that of a system of weakly coupled magnetic chains. In this picture a decrease of p corresponds with a decrease of the coupling between the chains. The differences in behaviour observed between the Ising systems on the one hand, and the (isotropic) XY or Heisenberg systems on the other, can then be explained by the fact that the intrachain correlation length depends exponentially on temperature for the Ising chain, whereas it depends much less strongly on temperature (∝ 1/T) for the XY and Heisenberg chains.     

A t-channel isospin analysis of the chew-low plot for NN → N(Nπ) interactions at 5.7 GeV/c

A new approach to the t-channel isospin analysis of ZN → Z′(Nπ) reactions is presented. This approach, useful for $\text{Z = N,}\text{N}\text{, K}{}^{\mathrm{?}}$ when only five independent sets of data are availables, is used to analyse data of $\text{N}\text{N →}\text{N}\text{(Nπ)}$ reactions obtained in a $\text{p}\text{p →}\text{N}\text{N}\text{π}$ experiment at $\text{5.7}\text{GeV}\text{/c}\text{and a}\text{p}\text{d →}\text{N}\text{Nπp}{}_{\mathrm{s}}$ experiment at 5.5 GeV/c. the t behaviour of the different isospin exchange amplitudes, suggests their exchange mechanism production. The mass spectrum, M_πN, of the contributions produced by exchanged isospin I_ex = 1, shows enhancements corresponding to N(1490) N(1670) and Δ(1230) isobars, while the mass spectrum for I_ex = 0 presents only a large bump at ～1350 MeV commonly identified as N¹(1400).     

CLL = (L,L; 0, 0) measurements and a structure due to a P partial wave in the pp system

Measurements of C_LL of pp elastic scattering near θ_c.m. = 90° at thirteen energies between 300 and 800 MeV are reported. These, together with previous values of C_NN, are used to extract values of two quantities, $\text{?}{}_{\mathrm{<mtext>s</mtext>}}$ and $\text{?}{}_{\mathrm{<mtext>t</mtext>}}$, which contain only spin-singlet and only coupled spin-triplet partial waves, respectively. The $\text{?}{}_{\mathrm{<mtext>s</mtext>}}$ curve, which is not dependent on C_LL, exhibits the behavior expected for the previously conjectured ¹D₂ resonance. The $\text{?}{}_{\mathrm{<mtext>t</mtext>}}$ curve also exhibits a resonance-like behavior, which could be due either to the ³P₀ or the ³P₂ partial wave.     

KMS condition in a Schrödinger picture of the dynamics

Given the C¹-algebra $\text{A}$ of observables, the KMS condition is formulated in terms of the time evolution α¹_t of a set $\text{S}$₀ ? $\text{S}$($\text{A}$) of “physical” states subject to certain natural conditions. α¹_t need not be defined by an automorphism group of $\text{A}$. It is shown that, for a KMS state ω, α¹_t induces a 1-automorphism α^ω_t of the von Neumann algebra π_ω($\text{A}$)″ generated by the representation π_ω belonging to ω.     

Evolution of the density for a chaotic map

For the discrete-time map x_t+11 = 4x_t(1?x_t) an exact, explicit expression is given for the time-dependent density r_t (x) evolving from a uniform initial density on (0,1). As t → ∞, r_t(x) approaches the known invariant density $\text{r(x) = 1/[π}\text{x(1?x)}\text{]}$.     

Absence of the second-order phase transitions in the dimerized Ising chains with spin larger than 12

A general spin S Ising chain interacting with a single phonon mode of the harmonic lattice is studied. The thermodynamics of the spin system is calculated exactly for S = 1, $\text{1}\text{2}$ and $\text{3}\text{2}$, while self-consistent equations for the induced lattice distortions are derived. It is demonstrated that for S >$\text{1}\text{2}$ there is no second-order phase transition, in contrast to the case S = $\text{1}\text{2}$ which was proved to have a tricritical point. This is found to cohere with the previous studies of the dimerized magnetic model chains.     

Optimal sum-rule inequalities for spin-12 compton scattering

A formalism appropriate for model-independent dispersion theoretical investigations of the (not necessarily forward) Compton scattering off $\text{spin}\text{-}\text{1}\text{2}$ hadronic targets, which fully exploits the analyticity properties of the amplitudes (to lowest order in electromagnetism) in ν² at fixed t ($\text{ν =}\text{1}\text{4}\text{(s ? u); s, t}$, u = Mandelstam variables), is developed. It relies on methods which are specific to boundary-value problems for analytic matrix-valued functions. An analytic factorization of the positive definite hermitian matrix associated with the bilinear expression of the unpolarized differential cross section (u.d.c.s.) in terms of the Bardeen-Tung (B.T.) invariant amplitudes is explicitly obtained. For t in a specified portion of the physical region, six new amplitudes describing the process are thereby constructed which have the same good analyticity structure in ν² as the (crossing symmetrized) B.T. amplitudes, while their connection with the usual helicity amplitudes is given by a matrix which is unitary on the unitarity cut. A bound on a certain integral over the u.d.c.s. above the first inelastic threshold, established in terms of the target's charge and anomalous magnetic moment, improves a previous weaker result, being now optimal under the information accepted as known.     

On the presence of the S4z-term in Fe(HCOO)2 · 2H2O

The magnetic specific heat of ferrous formate dihydrate is analysed on the basis of a model, $\text{S}{}_{\mathrm{A}}\text{=}\text{1}\text{2}$ and S_B = 2. The experimental result turns out to be well explained by the introduction of a large S⁴_z-term for B site ions.     

Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of 〈σ₀^x(t)σ_n^x(0)〉 and 〈σ₀^y(t)σ_n^y(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with $\text{0 ?}\text{n}\text{t}\text{<1}$, $\text{1 <}\text{n}\text{t}$, or $\text{t = n + n}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{(}\text{z}\text{2}\text{)}$ where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.     

Coupled channel study on the S-wave ππ → KK interaction

We perform a dispersion relation type calculation of the I = 0 S-wave amplitude g₀⁺ (t) for the process $\text{ππ →}\text{K}\text{K}$, in the region from t = 4μ² to t = (1100 MeV)². Crossing is imposed by generalizing the newly developed hyperbolic partial-wave relations to our reaction and by imposing them on our amplitude using experimental Kπ phase-shift information as input. Analyticity and unitarity is imposed by generalizing the formalism of BFP [1] for parametrizing partial-wave amplitudes. This readily allows us to impose the experimental $\text{ππ →}\text{K}\text{K}$ cross section. Finally the low energy behaviour is constrained to lie within certain limits recently deduced from fixed-tKπ dispersion relation studies [2] and including the current algebra prediction as a special case. We are able to resolve a previous controversy regarding the sign of Im g₀⁽⁺⁾ (t).     

Zero field steps in short Josephson junction

A theoretical investigation is carried out on the zero field current steps of a short Josephson junction under both the d.c. voltage V_d.c. and a.c. voltage V_a.c. cos ωt. The steps occur when the condition $\text{Ω + pω = 2Nω}{}_{\mathrm{n}}$ is fulfilled, where $\text{Ω = 2eV}{}_{\mathrm{d.c.}}\text{/}\text{h}\text{?}$, ω_n is the nth eigenfrequency in the eigenfrequency in the junction cavity, p and N are integers.     

The contribution to the specific heat from the spin-phonon interaction for (3d)n ions

The contribution, ΔC, to the specific heat arising from the spin-phonon interaction is calculated for general spin values. For a given set of spin-phonon coupling constants and cubic symmetry the ratio ΔC_max/ C(Schottky)_max for ions having S = 2 or $\text{5}\text{2}$ is one or two orders of magnitude greater than that for ions having S = 1 or $\text{3}\text{2}$. The relative low values of ΔC in the latter cases is traced to two distinct reasons, and the differences that the inclusion of a lower symmetry crystals field makes to the ratio is discussed.