From Disordered Crystal to Glass: Exact Theory

We calculate thermodynamic properties of a disordered model insulator, starting from the ideal simple-cubic lattice ($g = 0$) and increasing the disorder parameter $g$ to $\gg 1/2$. As in earlier Einstein- and Debye- approximations, there is a phase transition at $g_{c} = 1/2$. For $g<g_{c}$ the low-T heat-capacity $C \sim T^{3}$ whereas for $g>g_{c}$, $C \sim T$. The van Hove singularities disappear at {\em any finite $g$}. For $g>1/2$ we discover novel {\em fixed points} in the self-energy and spectral density of this model glass.Comment: Submitted to Phys. Rev. Lett., 8 pages, 4 figure

Electric Control of Spin Currents and Spin-Wave Logic

Spin waves in insulating magnets are ideal carriers for spin currents with low energy dissipation. An electric field can modify the dispersion of spin waves, by directly affecting, via spin-orbit coupling, the electrons that mediate the interaction between magnetic ions. Our microscopic calculations based on the super-exchange model indicate that this effect of the electric field is sufficiently large to be used to effectively control spin currents. We apply these findings to the design of a spin-wave interferometric device, which acts as a logic inverter and can be used as a building block for room-temperature, low-dissipation logic circuits.Comment: 4 pages, 3 figures, added the LL equation and the discussion on spin-wave-induced electric field, accepted by PR

Theory of optical spectral weights in Mott insulators with orbital degrees of freedom

Introducing partial sum rules for the optical multiplet transitions, we outline a unified approach to magnetic and optical properties of strongly correlated transition metal oxides. On the example of LaVO$_3$ we demonstrate how the temperature and polarization dependences of different components of the optical multiplet are determined by the underlying spin and orbital correlations dictated by the low-energy superexchange Hamiltonian. Thereby the optical data provides deep insight into the complex spin-orbital physics and the role played by orbital fluctuations.Comment: 6 pages, 3 figures, expanded versio

Inhomogeneous Nuclear Spin Flips

We discuss a feedback mechanism between electronic states in a double quantum dot and the underlying nuclear spin bath. We analyze two pumping cycles for which this feedback provides a force for the Overhauser fields of the two dots to either equilibrate or diverge. Which of these effects is favored depends on the g-factor and Overhauser coupling constant A of the material. The strength of the effect increases with A/V_x, where V_x is the exchange matrix element, and also increases as the external magnetic field B_{ext} decreases.Comment: 5 pages, 4 figures (jpg

Green's functions on finite lattices and their connection to the infinite lattice limit

It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices

From Effective Lagrangians, to Chiral Bags, to Skyrmions with the Large-N_c Renormalization Group

We explicitly relate effective meson-baryon Lagrangian models, chiral bags, and Skyrmions in the following way. First, effective Lagrangians are constructed in a manner consistent with an underlying large-N_c QCD. An infinite set of graphs dress the bare Yukawa couplings at *leading* order in 1/N_c, and are summed using semiclassical techniques. What emerges is a picture of the large-N_c baryon reminiscent of the chiral bag: hedgehog pions for r > 1/\Lambda patched onto bare nucleon degrees of freedom for r < 1/\Lambda, where the ``bag radius'' 1/\Lambda is the UV cutoff on the graphs. Next, a novel renormalization group (RG) is derived, in which the bare Yukawa couplings, baryon masses and hyperfine baryon mass splittings run with \Lambda. Finally, this RG flow is shown to act as a *filter* on the renormalized Lagrangian parameters: when they are fine-tuned to obey Skyrme-model relations the continuum limit \Lambda --> \infty exists and is, in fact, a Skyrme model; otherwise there is no continuum limit.Comment: Figures included (separate file). This ``replaced'' version corrects the discussion of backwards-in-time baryon

Anomalous dynamics in two- and three- dimensional Heisenberg-Mattis spin glasses

We investigate the spectral and localization properties of unmagnetized Heisenberg-Mattis spin glasses, in space dimensionalities $d=2$ and 3, at T=0. We use numerical transfer-matrix methods combined with finite-size scaling to calculate Lyapunov exponents, and eigenvalue-counting theorems, coupled with Gaussian elimination algorithms, to evaluate densities of states. In $d=2$ we find that all states are localized, with the localization length diverging as $\omega^{-1}$, as energy $\omega \to 0$. Logarithmic corrections to density of states behave in accordance with theoretical predictions. In $d=3$ the density-of-states dependence on energy is the same as for spin waves in pure antiferromagnets, again in agreement with theoretical predictions, though the corresponding amplitudes differ.Comment: RevTeX4, 9 pages, 9 .eps figure

Baryons with Many Colors and Flavors

Using recently-developed diagrammatic techniques, I derive some general results concerning baryons in the $1/N$ expansion, where $N$ is the number of QCD colors. I show that the spin-flavor relations which hold for baryons in the large-$N$ limit, as well as the form of the corrections to these relations at higher orders in $1/N$, hold even if $N_F / N \sim 1$, where $N_F$ is the number of light quark flavors. I also show that the amplitude for a baryon to emit $n$ mesons is $O(1 / N^{n / 2 - 1})$, and that meson loops attached to baryon lines are unsupressed in the large-$N$ limit, independent of $N_F$. For $N_F > 2$, there are ambiguities in the extrapolation away from $N = 3$ because the baryon flavor multiplets for a given spin grow with $N$. I argue that the $1/N$ expansion is valid for baryons with spin $O(1)$ and {\it arbitrary} flavor quantum numbers, including e.g. baryons with isospin and/or strangeness $O(N)$. This allows the formulation of a large-$N$ expansion in which it is not necessary to identify the physical baryons with particular large-$N$ states. $SU(N_F)$ symmetry can be made manifest to all orders in $1/N$, yet group theory factors must be evaluated explicitly only for $N_F = N = 3$. To illustrate this expansion, I consider the non-singlet axial currents, baryon mass splittings, and matrix elements of \mybar ss and \mybar s \gam_\mu \gam_5 s in the nucleon.Comment: 19 pages, plain TeX, 4 uuencoded postscrip figures, LBL-35539, NSF-ITP-94-4