Zero-temperature TAP equations for the Ghatak-Sherrington model

The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model are investigated. The spin-glass energy density (ground state) is determined as a function of the anisotropy crystal field $D$ for a large number of spins. This allows us to locate a first-order transition between the spin-glass and paramagnetic phases within a good accuracy. The total number of solutions is also determined as a function of $D$.Comment: 11 pages, 2 ps figures include

Effects of Random Biquadratic Couplings in a Spin-1 Spin-Glass Model

A spin-1 model, appropriated to study the competition between bilinear (J_{ij}S_{i}S_{j}) and biquadratic (K_{ij}S_{i}^{2}S_{j}^{2}) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins.Comment: 16 pages plus 2 ps figure

Gravitational waves from pulsars with measured braking index

We study the putative emission of gravitational waves (GWs) in particular for pulsars with measured braking index. We show that the appropriate combination of both GW emission and magnetic dipole brakes can naturally explain the measured braking index, when the surface magnetic field and the angle between the magnetic dipole and rotation axes are time dependent. Then we discuss the detectability of these very pulsars by aLIGO and the Einstein Telescope. We call attention to the realistic possibility that aLIGO can detect the GWs generated by at least some of these pulsars, such as Vela, for example.Comment: 6 pages and 4 figure

Coalescence Rate of Supermassive Black Hole Binaries Derived from Cosmological Simulations: Detection Rates for LISA and ET

The coalescence history of massive black holes has been derived from cosmological simulations, in which the evolution of those objects and that of the host galaxies are followed in a consistent way. The present study indicates that supermassive black holes having masses greater than $\sim 10^{9} M_{\odot}$ underwent up to 500 merger events along their history. The derived coalescence rate per comoving volume and per mass interval permitted to obtain an estimate of the expected detection rate distribution of gravitational wave signals ("ring-down") along frequencies accessible by the planned interferometers either in space (LISA) or in the ground (Einstein). For LISA, in its original configuration, a total detection rate of about $15 yr^{-1}$ is predicted for events having a signal-to-noise ratio equal to 10, expected to occur mainly in the frequency range $4-9 mHz$. For the Einstein gravitational wave telescope, one event each 14 months down to one event each 4 years is expected with a signal-to-noise ratio of 5, occurring mainly in the frequency interval $10-20 Hz$. The detection of these gravitational signals and their distribution in frequency would be in the future an important tool able to discriminate among different scenarios explaining the origin of supermassive black holes.Comment: 18 pages, 7 figures, to appear in the IJMP