Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature

We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finite-many hierarchies are unstable and only the scheme with infinite-many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing the number of hierarchies.Comment: REVTeX4, 11 pages, no figure

On-Chip Microwave Quantum Hall Circulator

Circulators are non-reciprocal circuit elements integral to technologies including radar systems, microwave communication transceivers, and the readout of quantum information devices. Their non-reciprocity arises from the interference of microwaves over the centimetre-scale of the signal wavelength in the presence of bulky magnetic media that break time-reversal symmetry. Here we realize a completely passive on-chip microwave circulator with size one-thousandth the wavelength by exploiting the chiral, slow-light response of a 2-dimensional electron gas (2DEG) in the quantum Hall regime. For an integrated GaAs device with 330 um diameter and 1 GHz centre frequency, a non-reciprocity of 25 dB is observed over a 50 MHz bandwidth. Furthermore, the direction of circulation can be selected dynamically by varying the magnetic field, an aspect that may enable reconfigurable passive routing of microwave signals on-chip

Absence of anomalous negative lattice-expansion for polycrystalline sample of Tb2Ti2O7

High resolution X-ray powder-diffraction experiments on a well-characterized polycrystalline sample of the spin liquid Tb2Ti2O7 reveal that it shows normal positive thermal-expansion above 4 K, which does not agree with the intriguing anomalous negative thermal-expansion due to a magneto-elastic coupling reported for a single crystal sample below 20 K. We also performed a Rietveld profile refinement of a powder-diffraction pattern taken at a room temperature, and confirmed that it is consistent with the fully ordered cubic pyrochlore structure.Comment: 2 pages, 3 figure

Two 2MASS-Selected Young Stellar Clusters: Photometry, Spectroscopy, and the IMF

We present near-infrared J, H, and K_s images and K-band spectroscopy of two newly discovered stellar clusters at different stages of evolution. Our spectra suggest the presence of massive YSOs in the heavily embedded cluster in the star-forming region near radio source G353.4-0.4 and an O5-O6V star in the cluster near radio source G305+00.2. We determine a K-band luminosity function (KLF) for both clusters and an initial mass function (IMF) for the cluster near G305+00.2. The derived IMF slope is -1.5 if the KLF is used to derive the IMF and is -0.98 if the color-magnitude diagram and spectra are used. The more reliable CMD-based slope is flatter than the Salpeter value usually found for stellar clusters. We find that using the KLF alone to derive an IMF is likely to produce an overly steep slope in stellar clusters subject to variable extinction.Comment: 16 pages, 18 figures, accepted to A

Magnetic Ordering in the Spin-Ice Candidate Ho2_2Ru2_2O7_7

Neutron scattering measurements on the spin-ice candidate material Ho$_2$Ru$_2$O$_7$ have revealed two magnetic transitions at T $\sim$ 95 K and T $\sim$ 1.4 K to long-range ordered states involving the Ru and Ho sublattices, respectively. Between these transitions, the Ho$^{3+}$ moments form short-ranged ordered spin clusters. The internal field provided by the ordered S=1 Ru$^{4+}$ moments disrupts the fragile spin-ice state and drives the Ho$^{3+}$ moments to order. We have directly measured a slight shift in the Ho$^{3+}$ crystal field levels at 95 K from the Ru ordering.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Letter

A Deep Multicolor Survey. VI. Near-Infrared Observations, Selection Effects, and Number Counts

I present near-infrared J (1.25um), H (1.65um), and K (2.2um) imaging observations of 185 square arcminutes in 21 high galactic latitude fields. These observations reach limiting magnitudes of J ~ 21 mag, H ~ 20 mag and K ~ 18.5 mag. The detection efficiency, photometric accuracy and selection biases as a function of integrated object brightness, size, and profile shape are quantified in detail. I evaluate several popular methods for measuring the integrated light of faint galaxies and show that only aperture magnitudes provide an unbiased measure of the integrated light that is independent of apparent magnitude. These J, H, and K counts and near-infrared colors are in best agreement with passive galaxy formation models with at most a small amount of merging (for Omega_M = 0.3, Omega_Lambda = 0.7).Comment: AJ Accepted (Feb 2001). 28 pages, 7 embedded ps figures, AASTEX5. Minor changes to submitted version. Also available at http://www.astronomy.ohio-state.edu/~martini/pubs

Optimal static and dynamic recycling of defective binary devices

The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular, the region in the parameter space where there is almost surely at least one fully-working subset. Dynamic recycling of a flux of imperfect binary components leads to zero wastage.Comment: 14 pages, 15 figure

A Search for Molecular Gas in GHz Peaked Spectrum Radio Sources

We present searches for molecular gas (CO, OH, CS, and Ammonia) in six GHz Peaked Spectrum (GPS) radio sources. We do not detect gas in any source and place upper limits on the mass of molecular gas which are generally in the range 1E9 to a few times 1E10 solar masses. These limits are consistent with the following interpretations: (1) GPS sources do not require very dense gas in their hosts, and (2) The GPS sources are unlikely to be confined by dense gas and will evolve to become larger radio sources

Symmetries of Differential Equations via Cartan's Method of Equivalence

We formulate a method of computing invariant 1-forms and structure equations of symmetry pseudo-groups of differential equations based on Cartan's method of equivalence and the moving coframe method introduced by Fels and Olver. Our apparoach does not require a preliminary computation of infinitesimal defining systems, their analysis and integration, and uses differentiation and linear algebra operations only. Examples of its applications are given.Comment: 15 pages, LaTeX 2.0