Finite-size spin-wave theory of a collinear antiferromagnet

The ground-state and low-energy properties of the two-dimensional $J_1{-}J_2$ Heisenberg model in the collinear phase are investigated using finite-size spin-wave theory [Q. F. Zhong and S. Sorella, {\em Europhys. Lett.} {\bf 21}, 629 (1993)], and Lanczos exact diagonalizations. For spin one-half -- where the effects of quantization are the strongest -- the spin-wave expansion turns out to be quantitatively accurate for $J_2/J_1\gtrsim 0.8$. In this regime, both the magnetic structure factor and the spin susceptibility are very close to the spin-wave predictions. The spin-wave estimate of the order parameter in the collinear phase, $m^\dagger\simeq 0.3$, is in remarkable agreement with recent neutron scattering measurements on ${\rm Li_2VOSiO_4}$.Comment: 10 pages, 3 figure

Star-cumulants of free unitary Brownian motion

We study joint free cumulants of u_t and u_t^{*}, where u_t is a free unitary Brownian motion at time t. We determine explicitly some special families of such cumulants. On the other hand, for a general joint cumulant of u_t and u_t^{*}, we "calculate the derivative" for t going to infinity, when u_t approaches a Haar unitary. In connection to the latter calculation we put into evidence an "infinitesimal determining sequence" which naturally accompanies an arbitrary R-diagonal element in a tracial *-probability space.Comment: 35 pages. This version has added details in Sections 5 and

Incommensurate, helical spin ground states on the Hollandite lattice

We present a model of classical Heisenberg spins on a Hollandite lattice, which has been developed to describe the magnetic properties of $\alpha$-MnO$_2$ and similar compounds. The model has nearest neighbor interacting spins, however the strength and the sign of spin-spin interactions is anisotropic and depends on the nature of the bonds. Our analysis shows that the Hollandite lattice supports four different incommensurate and helical magnetic ground states depending on the relative strengths and signs of spin-spin interactions. We show that the incommensurate helical ground states appear due to the geometrical frustration present in the model. We demonstrate that each of the four helical incommensurate magnetic phases are continuously connected to four different collinear antiferromagnetic ground states as the strength of spin-spin interaction along some bonds is increased. The present results give support to the presence of helical states that have been previously suggested experimentally for Hollandite compounds. We provide an in-depth analysis of the magnetic form factors for each helical phase and describe how it could be used to identify each of these phases in neutron diffraction experiments.Comment: 11 pages, 8 figure

Andean tectonics: Implications for Satellite Geodesy

Current knowledge and theories of large scale Andean tectonics as they relate to site planning for the NASA Crustal Dynamics Program's proposed high precision geodetic measurements of relative motions between the Nazca and South American plates are summarized. The Nazca Plate and its eastern margin, the Peru-Chile Trench, is considered a prototype plate marked by rapid motion, strong seismicity and well defined boundaries. Tectonic activity across the Andes results from the Nazca Plate subducting under the South American plate in a series of discrete platelets with different widths and dip angles. This in turn, is reflected in the tectonic complexity of the Andes which are a multitutde of orogenic belts superimposed on each other since the Precambrian. Sites for Crustal Dynamics Program measurements are being located to investigate both interplate and extraplate motions. Observing operations have already been initiated at Arequipa, Peru and Easter Island, Santiago and Cerro Tololo, Chile. Sites under consideration include Iquique, Chile; Oruro and Santa Cruz, Bolivia; Cuzco, Lima, Huancayo and Bayovar, Peru; and Quito and the Galapagos Islands, Ecuador. Based on scientific considerations, Santa Cruz, Huancayo (or Lima), Quito and the Galapagos Islands should be replaced by Isla San Felix, Chile; Brazilia or Petrolina, Brazil; and Guayaquil, Ecuador. If resources permit, additional important sites would be Buenaventura and Villavicencio or Puerto La Concordia, Colombia; and Mendoza and Cordoba, Argentina

Slow Coarsening in an Ising Chain with Competing Interactions

We investigate the zero-temperature coarsening dynamics of a chain of Ising spins with a nearest-neighbor ferromagnetic and an nth-neighbor antiferromagnetic interactions. For sufficiently large antiferromagnetic interaction, the ground state consists of $n$ consecutive up spins followed by n down spins, etc. We show that the asymptotic coarsening into this ground state is governed by a multispecies reactive gas of elementary excitations. The basic elementary excitations are identified and each decays at a different power-law rate in time. The dominant excitations are domains of n+1 spins which diffuse freely and disappear through processes which are effectively governed by (n+1)-particle annihilation. This implies that the ground state is approached slowly with time, as t^{-1/n}.Comment: 7 pages, 2 figures, revtex 2-column format, submitted to J. Phys.