On the positivity of correlations in nonequilibrium spin systems

We consider Ising spin systems, equivalently lattice gases evolving under discrete- or continuous-time Markov processes, i.e., stochastic cellular automata or interacting particle systems. We show that for certain spin-flip probabilities or rates and suitable initial states the expectation values of products of spin variables taken at equal or different times are nonnegative; they satisfy the same inequalities as the equal-time correlations of ferromagnetic systems in equilibrium (first Griffiths inequality). Extensions of FKG inequalities to time-displaced correlations are also discussed.     

Block averaging renormalization group for lattice and continuum euclidean fermions: Expected and unexpected results

Simple relations, given by the trace and supertrace, between expectation values of tensor operators connected with a Lie superalgebra g are shown to be generated by the Weyl group of a Lie algebra 0 acting on a Lie superalgebra.     

Spin relaxation times in disordered graphene

We consider two mechanisms of spin relaxation in disordered graphene. i) Spin relaxation due to curvature spin orbit coupling caused by ripples. ii) Spin relaxation due to the interaction of the electronic spin with localized magnetic moments at the edges. We obtain analytical expressions for the spin relaxation times τ_SO and τ_J due to both mechanisms and estimate their values for realistic parameters of graphene samples. We obtain that spin relaxation originating from these mechanisms is very weak and spin coherence is expected in disordered graphene up to samples of length .     

A perturbative approach to spectrum and correlation functions of the chiral Potts model

The massive high-temperature phase of the chiral Potts quantum chain is studied using perturbative methods. For the ₃-chain we present high-temperature expansions for the ground-state energy and the dispersion relations of the two single-particle states as well as two-particle states at general values of the parameters. We also present a perturbative argument showing that a large class of massive _n-spin quantum chains have quasiparticle spectra withn-1 fundamental particles. It is known from earlier investigations that—at special values of the parameters—some of the fundamental particles exist only for limited ranges of the momentum. In these regimes our argument is not rigorous, as one can conclude from a discussion of the radius of convergence of the perturbation series. We also derive correlation functions from a perturbative evaluation of the ground-state for the ₃-chain. In addition to an exponential decay we observe an oscillating contribution. The oscillation length seems to be related to the asymmetry of the dispersion relations. We show that this relation is exact at special values of the parameters for general _n using a form factor expansion.     

Spin waves on chains of YIG particles: dispersion relations,Faraday rotation,and power transmission

We calculate the dispersion relations for spin waves on a periodic chain of spherical or cylindrical Yttrium Iron Garnet (YIG) particles. We use the quasistatic approximation, appropriate when kd ? 1, where k is the wave number and d the interparticle spacing. In this regime, because of the magnetic dipole-dipole interaction between the localized magnetic excitations on neighboring particles, dispersive spin waves can propagate along the chain. The waves are analogous to plasmonic waves generated by electric dipole-dipole interactions between plasmons on neighboring metallic particles. The spin waves can be longitudinal (L), transverse (T), or elliptically polarized. We find that a linearly polarized spin wave undergoes a Faraday rotation as it propagates along the chain. The amount of Faraday rotation can be tuned by varying the off-diagonal component of the permeability tensor. We also discuss the possibility of wireless power transmission along the chain using these coupled spin waves.     

Uncovering the features of spin dynamics in hadronic physics

We summarize the program pursued by Michael J. Moravcsik and the authors on spin amplitude analyses and interpretation. We present the recent observations that phase histograms reveal striking peaks corresponding to spin amplitudes that tend to have definite simple phase relations. An interpretation is proposed in which the spin amplitudes receive a coherent and an incoherent contribution over large ranges of energies and angles. Continuing research directions are reported.Dedicated to the memory of Michael J. Moravcsik, whose contribution to this work, our research, and spin physics is immeasurable     

On the dynamics of a quantum system which is classically chaotic

We investigate the dynamics of one anisotropic spin in an external time-dependent magnetic field. The classical dynamics of the system is nonintegrable (and very similar to the standard map). We present results on this model for a quantum spin (i.e. for finite values of the spin lengthS). In particular we discuss the semiclassical regime,S1, using the concept of Wigner functions to define a suitable probability distribution. In regular regions of phase space the time evolution of the probability distribution shows an algebraic decay of correlations as in quantum mechanics. In chaotic regions of phase space it is characterised by a positive Lyapunov exponent which depends onS. In these regions semiclassical trajectories coincide with classical ones fort <₀ where ₀InS.     

Bilinear quantum Monte Carlo: Expectations and energy differences

We propose a bilinear sampling algorithm in the Green's function Monte Carlo for expectation values of operators that do not commute with the Hamiltonian and for differences between eigenvalues of different Hamiltonians. The integral representations of the Schrödinger equations are transformed into two equations whose solution has the form _a(x) t(x, y)_b(y), where _a and _b are the wavefunctions for the two related systems andt(x, y) is a kernel chosen to couplex andy. The Monte Carlo process, with random walkers on the enlarged configuration spacex y, solves these equations by generating densities whose asymptotic form is the above bilinear distribution. With such a distribution, exact Monte Carlo estimators can be obtained for the expectation values of quantum operators and for energy differences. We present results of these methods applied to several test problems, including a model integral equation, and the hydrogen atom.     

Electronic structure of the Sr0.4Ca13.6Cu24O41 incommensurate compound

We extracted, from strongly-correlated ab-initio calculations, a complete model for the chain subsystem of the Sr0.4Ca13.6Cu24O41 incommensurate compound. A second neighbor t-J+V model has been determined as a function of the fourth crystallographic parameter , for both low and room temperature crystallographic structures. The analysis of the obtained model shows the crucial importance of the structural modulations on the electronic structure through the on-site energies and the magnetic interactions. The structural distortions are characterized by their long range effect on the cited parameters that hinder the reliability of analyses such as BVS. One of the most striking results is the existence of antiferromagnetic nearest-neighbor interactions for metal-ligand-metal angles of 90. A detailed analysis of the electron localization and spin arrangement is presented as a function of the chain to ladder hole transfer and of the temperature. The obtained spin arrangement is in agreement with antiferromagnetic correlations in the chain direction at low temperature.     

Thermodynamics of the quantum spin-S XXZ chain

The thermodynamics of the spin-S anisotropic quantum XXZ chain with arbitrary value of S and unitary norm, in the high-temperature regime, is reported. The single-ion anisotropy term and the interaction with an external magnetic field in the z-direction are taken into account. We obtain, for arbitrary value of S, the β-expansion of the Helmholtz free energy of the model up to order β⁶ and show that it actually depends on . Its classical limit is obtained by simply taking S→∞. At h=0 and D=0, our high temperature expansion of the classical model coincides with Joyce’s exact solution [11]. We study, in the high temperature region, some thermodynamic quantities such as the specific heat and the magnetic susceptibility as functions of spin and verify for which values of S those thermodynamic functions behave classically. Their finite temperature behavior is inferred from interpolation of their high- and low-temperature behavior, and shown to be in good agreement with numerical results. The finite temperature behavior is shown for higher values of spin.     

The Kac Version of the Sherrington–Kirkpatrick Model at High Temperatures

We study the Kac version of the Sherrington–Kirkpatrick (SK) model of a spin glass, i.e., a spin glass with long- but finite-range interaction on and Gaussian mean zero couplings. We prove that for all < 1, the free energy of this model converges to that of the SK model as the range of the interaction tends to infinity. Moreover, we prove that for all temperatures for which the infinite-volume Gibbs state is unique, the free energy scaled by the square root of the volume converges to a Gaussian with variance c _, , where ^–1 is the range of the interaction. Moreover, at least for almost all values of , this variance tends to zero as goes to zero, the value in the SK model. We interpret our finding as a weak indication that at least at high temperatures, the SK model can be seen as a reasonable asymptotic model for lattice spin glasses.     

Effect of the block-spin configuration on the location of βc in two-dimensional Ising modelsin two-dimensional Ising models

We consider the nearest neighbor Ising model on the 2D square lattice and divide the lattice into 2 by 2 blocks. Each block is assigned one spin value (1 or –1) and these block spin values are kept fixed. We then impose the majority rule and look at the effect on the phase transition that was present in the original unconstrained spin system. We find that for the checkerboard block-spin configuration, Monte Carlo simulations show that _c is close to 1, which, compared to the original nearest neighbor Ising _c = 0.44..., shows that the critical temperature has been reduced by more than one half. For none of the other 11 block-spin configurations that we have considered is there any indication of a phase transition in the constrained system of original spins.     

Remarks on the Balance Relations for the Two-Dimensional Navier–Stokes Equation with Random Forcing

We use the balance relations for the stationary in time solutions of the randomly forced 2D Navier-Stokes equations, found in [10], to study these solutions further. We show that the vorticity ξ(t,x) of a stationary solution has a finite exponential moment, and that for any the expectation of the integral of over the level-set , up to a constant factor equals the expectation of the integral of over the same set.     

Bethe ansatz results for Hubbard chains with toroidal boundary conditions

We solve exactly the problem of a one-dimensional repulsive-U Hubbard chain with toroidal boundary conditions (HTB) using the Bethe ansatz approach. We calculate analytically the finite-size corrections to the ground-state energy in the half-filled case and use this expression to derive charge and spin stiffnesses with no assumptions. We then use a particle-hole transformation to calculate the finite-size corrections for the half-filledattractive- U case, and again derive the resulting expressions for the charge and spin stiffnesses. Lastly, we discuss how the repulsive-U corrections relate to those of a Heisenberg model with toroidal boundary conditions.On leave from Departamento de Fisica, Universidade Federal de S. Carlos, S. Carlos, 13560, Brazil.     

Kramers-Krönig relations in nonlinear optics

We review dispersion relations, which relate the real part of the optical susceptibility (refraction) to the imaginary part (absorption). We derive and discuss these relations as applied to nonlinear optical systems. It is shown that in the nonlinear case, for self-action effects the correct form for such dispersion relations is nondegenerate, i.e. it is necessary to use multiple frequency arguments. Nonlinear dispersion relations have been shown to be very useful as they usually only require integration over a limited frequency range (corresponding to frequencies at which the absorption changes), unlike the conventional linear Kramers-Krönig relation which requires integration over all absorbing frequencies. Furthermore, calculation of refractive index changes using dispersion relations is easier than a direct calculation of the susceptibility, as transition rates (which give absorption coefficients) are, in general, far easier to calculate than the expectation value of the optical polarization. Both resonant (generation of some excitation that is long lived compared with an optical period) and nonresonant instantaneous optical nonlinearities are discussed, and it is shown that the nonlinear dispersion relation has a common form and can be understood in terms of the linear Kramers-Krönig relation applied to a new system consisting of the material plus some perturbation. We present several examples of the form of this external perturbation, which can be viewed as the pump in a pump-probe experiment. We discuss the two-level saturated atom model and bandfilling in semiconductors among others for the resonant case. For the nonresonant case some recent work is included where the electronic nonlinear refractive coefficient,n ₂, is determined from the nonlinear absorption processes of two-photon absorption, Raman transitions and the a.c. Stark effect. We also review how the dispersion relations can be extended to give alternative forms for frequency summation which, for example, allows the real and imaginary parts of ⁽²⁾ to be related.     

Variational theory for correlated lattice fermions in high dimensions

A diagrammatic approach to the evaluation of correlated variational wave functions for strongly interacting fermions is presented. Diagrammatic rules for the calculation of the one-particle density matrix and the Hubbard interaction are derived which are valid for arbitraryd-dimensional lattices. An exact evaluation of expectation values is performed in the limitd=. The wellknown Gutzwiller approximation is seen to become the exact result for the expectation value of the Hubbard Hamiltonian in terms of the Gutzwiller wave function ind=. An efficient procedure to correct the Gutzwiller approximation in finite dimensions is developed. A detailed discussion of expectation values ind= in terms of explicit antiferromagnetic wave functions is given. Thereby an approximate result for the ground state energy of the Hubbard model, obtained recently within a slave-boson approach, is recovered.     

Classical Heisenberg antiferromagnets with nearest and next-nearest neighbor interactions on the face-centered cubic lattice: a model for EuTe?

Magnetic properties of the Heisenberg antiferromagnet with spin quantum numberS on the face-centered cubic lattice are studied as function of temperature and magnetic field, using molecular field approximation and Monte Carlo methods. In order to model Europiumtelluride, we use isotropic exchange interactions between nearest- and nextnearest neighbors; the values of these exchange constants are taken from experiments. In addition, a pseudo-dipolar anisotropy (truncated after the next-nearest neighbor distance) is included; the molecular field calculations also are performed with the full dipolar of real EuTe in two respects: the structure in zero magnetic field involves 8 sublattices in the model rather than only two; the bicritical point, above which in the temperatureT magnetic fieldH plane the spin flop phase appears, occurs atH=0 in the model rather than at nonzero field. Possible additional interactions responsible for these discrepancies are discussed. Applying finite size scaling techniques we give also a preliminary analysis of the critical behavior of the model.     

Gibbsian Hypothesis in Turbulence

We show that Kolmogorov multipliers in turbulence cannot be statistically independent of others at adjacent scales (or even a finite range apart) by numerical simulation of a shell model and by theory. As the simplest generalization of independent distributions, we suppose that the steady-state statistics of multipliers in the shell model are given by a translation-invariant Gibbs measure with a short-range potential, when expressed in terms of suitable spin variables: real-valued spins that are logarithms of multipliers and XY-spins defined by local dynamical phases. Numerical evidence is presented in favor of the hypothesis for the shell model, in particular novel scaling laws and derivative relations predicted by the existence of a thermodynamic limit. The Gibbs measure appears to be in a high-temperature, unique-phase regime with paramagnetic spin order.