A strong-coupling analysis of two-dimensional O(N) sigma models with N≥3N\geq 3 on square, triangular and honeycomb lattices

Recently-generated long strong-coupling series for the two-point Green's functions of asymptotically free ${\rm O}(N)$ lattice $\sigma$ models are analyzed, focusing on the evaluation of dimensionless renormalization-group invariant ratios of physical quantities and applying resummation techniques to series in the inverse temperature $\beta$ and in the energy $E$. Square, triangular, and honeycomb lattices are considered, as a test of universality and in order to estimate systematic errors. Large-$N$ solutions are carefully studied in order to establish benchmarks for series coefficients and resummations. Scaling and universality are verified. All invariant ratios related to the large-distance properties of the two-point functions vary monotonically with $N$, departing from their large-$N$ values only by a few per mille even down to $N=3$.Comment: 53 pages (incl. 5 figures), tar/gzip/uuencode, REVTEX + psfi

Investigation of a temperature tolerant InGaP (GaInP) converter layer for a 63Ni betavoltaic cell

A prototype InGaP p+–i–n+ mesa photodiode was studied for its potential as the energy conversion device in a 63Ni betavoltaic cell; its electrical performance was analysed across the temperature range −20 °C to 100 °C. The results show that the InGaP detector when illuminated with a laboratory 63Ni radioisotope beta particle source had a maximum output power of 0.92 pW at −20 °C, this value decreased at higher temperatures. A decrease in the open circuit voltage and in the cell internal conversion ef ciency were also observed when the temperature was increased: at −20 °C, the open circuit voltage and the cell internal conversion ef ciency had values of 0.69 V and 4%, respectively. A short circuit current of 4.5 pA was measured at −20 °C

Temperature study of Al0.52In0.48P detector photon counting X-ray spectrometer

A prototype 200 μm diameter Al0.52In0.48P p+-i-n+ mesa photodiode (2 μm i-layer) was characterised at temperatures from 100 °C to −20 °C for the development of a temperature tolerant photon counting X-ray spectrometer. At each temperature, X-ray spectra were accumulated with the AlInP detector reverse biased at 0 V, 5 V, 10 V, and 15 V and using different shaping times. The detector was illuminated by an 55Fe radioisotope X-ray source. The best energy resolution, as quantified by the full width at half maximum (FWHM) at 5.9 keV, was observed at 15 V for all the temperatures studied; at 100 °C, a FWHM of 1.57 keV was achieved, and this value improved to 770 eV FWHM at −20 °C. System noise analysis was also carried out, and the different noise contributions were computed as functions of temperature. The results are the first demonstration of AlInP's suitability for photon counting X-ray spectroscopy at temperatures other than ≈20 °C

Evidence of strong antiferromagnetic coupling between localized and itinerant electrons in ferromagnetic Sr2FeMoO6

Magnetic dc susceptibility ($\chi$) and electron spin resonance (ESR) measurements in the paramagnetic regime, are presented. We found a Curie-Weiss (CW) behavior for $\chi$(T) with a ferromagnetic $\Theta = 446(5)$ K and $\mu_{eff} = 4.72(9) \mu_{B}/f.u.$, this being lower than that expected for either $Fe^{3+}(5.9\mu_{B})$ or $Fe^{2+}(4.9\mu_{B})$ ions. The ESR g-factor $g = 2.01(2)$, is associated with $Fe^{3+}$. We obtained an excellent description of the experiments in terms of two interacting sublattices: the localized $Fe^{3+}$ ($3d^{5}$) cores and the delocalized electrons. The coupled equations were solved in a mean-field approximation, assuming for the itinerant electrons a bare susceptibility independent on $T$. We obtained $\chi_{e}^{0} = 3.7$ $10^{-4}$ emu/mol. We show that the reduction of $\mu_{eff}$ for $Fe^{3+}$ arises from the strong antiferromagnetic (AFM) interaction between the two sublattices. At variance with classical ferrimagnets, we found that $\Theta$ is ferromagnetic. Within the same model, we show that the ESR spectrum can be described by Bloch-Hasegawa type equations. Bottleneck is evidenced by the absence of a $g$-shift. Surprisingly, as observed in CMR manganites, no narrowing effects of the ESR linewidth is detected in spite of the presence of the strong magnetic coupling. These results provide evidence that the magnetic order in $Sr_{2}FeMoO_{6}$ does not originates in superexchange interactions, but from a novel mechanism recently proposed for double perovskites

N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also known as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] on the sc and the bcc lattices are extended to order beta^{21} for arbitrary N. The series for the second field derivative of the susceptibility is extended to order beta^{17}. An analysis of the newly computed series for the susceptibility and the (second moment) correlation length yields updated estimates of the critical parameters for various values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the Heisenberg model]. For all values of N, we confirm a good agreement with the present renormalization group estimates. A study of the series for the other observables will appear in a forthcoming paper.Comment: Revised version to appear in Phys. Rev. B Sept. 1997. Revisions include an improved series analysis biased with perturbative values of the scaling correction exponents computed by A. I. Sokolov. Added a reference to estimates of exponents for the Ising Model. Abridged text of 19 pages, latex, no figures, no tables of series coefficient

High precision Monte Carlo study of the 3D XY-universality class

We present a Monte Carlo study of the two-component $\phi^4$ model on the simple cubic lattice in three dimensions. By suitable tuning of the coupling constant $\lambda$ we eliminate leading order corrections to scaling. High statistics simulations using finite size scaling techniques yield $\nu=0.6723(3)[8]$ and $\eta=0.0381(2)[2]$, where the statistical and systematical errors are given in the first and second bracket, respectively. These results are more precise than any previous theoretical estimate of the critical exponents for the 3D XY universality class.Comment: 13 page

Hamiltonian Dynamics and the Phase Transition of the XY Model

A Hamiltonian dynamics is defined for the XY model by adding a kinetic energy term. Thermodynamical properties (total energy, magnetization, vorticity) derived from microcanonical simulations of this model are found to be in agreement with canonical Monte-Carlo results in the explored temperature region. The behavior of the magnetization and the energy as functions of the temperature are thoroughly investigated, taking into account finite size effects. By representing the spin field as a superposition of random phased waves, we derive a nonlinear dispersion relation whose solutions allow the computation of thermodynamical quantities, which agree quantitatively with those obtained in numerical experiments, up to temperatures close to the transition. At low temperatures the propagation of phonons is the dominant phenomenon, while above the phase transition the system splits into ordered domains separated by interfaces populated by topological defects. In the high temperature phase, spins rotate, and an analogy with an Ising-like system can be established, leading to a theoretical prediction of the critical temperature $T_{KT}\approx 0.855$.Comment: 10 figures, Revte

Critical behaviour and scaling functions of the three-dimensional O(6) model

We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3 lattices within the critical region at zero magnetic field, as well as at finite magnetic field on the critical isotherm and for several fixed couplings in the broken and the symmetric phase. We obtain from the Binder cumulant at vanishing magnetic field the critical coupling J_c=1.42865(3). The universal value of the Binder cumulant at this point is g_r(J_c)=-1.94456(10). At the critical coupling, the critical exponents \gamma=1.604(6), \beta=0.425(2) and \nu=0.818(5) are determined from a finite-size-scaling analysis. Furthermore, we verify predicted effects induced by massless Goldstone modes in the broken phase. The results are well described by the perturbative form of the model's equation of state. Our O(6)-result is compared to the corresponding Ising, O(2) and O(4) scaling functions. Finally, we study the finite-size-scaling behaviour of the magnetisation on the pseudocritical line.Comment: 13 pages, 20 figures, REVTEX, fixed an error in the determination of R_\chi and changed the corresponding line in figure 13

Geometric Approach to Lyapunov Analysis in Hamiltonian Dynamics

As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of the Hamiltonian function. To separate out these two directions and to apply Lyapunov analysis effectively in directions for which Lyapunov exponents are not trivial, a geometric method is proposed for natural Hamiltonian systems, in particular. In this geometric method, Hamiltonian flows of a natural Hamiltonian system are regarded as geodesic flows on the cotangent bundle of a Riemannian manifold with a suitable metric. Stability/instability of the geodesic flows is then analyzed by linearized equations of motion which are related to the Jacobi equations on the Riemannian manifold. On some geometric setting on the cotangent bundle, it is shown that along a geodesic flow in question, there exist Lyapunov vectors such that two of them are in the two marginal directions and the others orthogonal to the marginal directions. It is also pointed out that Lyapunov vectors with such properties can not be obtained in general by the usual method which uses linearized Hamilton's equations of motion. Furthermore, it is observed from numerical calculation for a model system that Lyapunov exponents calculated in both methods, geometric and usual, coincide with each other, independently of the choice of the methods.Comment: 22 pages, 14 figures, REVTeX

Renormalized couplings and scaling correction amplitudes in the N-vector spin models on the sc and the bcc lattices

For the classical N-vector model, with arbitrary N, we have computed through order \beta^{17} the high temperature expansions of the second field derivative of the susceptibility \chi_4(N,\beta) on the simple cubic and on the body centered cubic lattices. (The N-vector model is also known as the O(N) symmetric classical spin Heisenberg model or, in quantum field theory, as the lattice O(N) nonlinear sigma model.) By analyzing the expansion of \chi_4(N,\beta) on the two lattices, and by carefully allowing for the corrections to scaling, we obtain updated estimates of the critical parameters and more accurate tests of the hyperscaling relation d\nu(N) +\gamma(N) -2\Delta_4(N)=0 for a range of values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the classical Heisenberg model]. Using the recently extended series for the susceptibility and for the second correlation moment, we also compute the dimensionless renormalized four point coupling constants and some universal ratios of scaling correction amplitudes in fair agreement with recent renormalization group estimates.Comment: 23 pages, latex, no figure