Earth's gravity field mapping requirements and concept

A future sensor is considered for mapping the Earth's gravity field to meet future scientific and practical requirements for earth and oceanic dynamics. These are approximately + or - 0.1 to 10 mgal over a block size of about 50 km and over land and an ocean geoid to 1 to 2 cm over a distance of about 50 km. To achieve these values requires a gravity gradiometer with a sensitivity of approximately 10 to the -4 power EU in a circular polar orbiting spacecraft with an orbital altitude ranging 160 km to 180 km

Proof of a conjecture of N. Konno for the 1D contact process

Consider the one-dimensional contact process. About ten years ago, N. Konno stated the conjecture that, for all positive integers $n,m$, the upper invariant measure has the following property: Conditioned on the event that $O$ is infected, the events $\{$All sites $-n,...,-1$ are healthy$\}$ and $\{$All sites $1,...,m$ are healthy$\}$ are negatively correlated. We prove (a stronger version of) this conjecture, and explain that in some sense it is a dual version of the planar case of one of our results in \citeBHK.Comment: Published at http://dx.doi.org/10.1214/074921706000000031 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

On effects of regular S=1 dilution of S=1/2 antiferromagnetic Heisenberg chains by a quantum Monte Carlo simulation

The effects of regular S=1 dilution of S=1/2 isotropic antiferromagnetic chain are investigated by the quantum Monte Carlo loop/cluster algorithm. Our numerical results show that there are two kinds of ground-state phases which alternate with the variation of $S^1=1$ concentration. When the effective spin of a unit cell is half-integer, the ground state is ferrimagnetic with gapless energy spectrum and the magnetism becomes weaker with decreasing of the $S^1$ concentration $\rho = 1/M$. While it is integer, a non-magnetic ground state with gaped spectrum emerges and the gap gradually becomes narrowed as fitted by a relation of $\Delta \approx 1.25\sqrt{\rho}$.Comment: 6 pages, 9 figure

A DMRG Study of Low-Energy Excitations and Low-Temperature Properties of Alternating Spin Systems

We use the density matrix renormalization group (DMRG) method to study the ground and low-lying excited states of three kinds of uniform and dimerized alternating spin chains. The DMRG procedure is also employed to obtain low-temperature thermodynamic properties of these systems. We consider a 2N site system with spins $s_1$ and $s_2$ alternating from site to site and interacting via a Heisenberg antiferromagnetic exchange. The three systems studied correspond to $(s_1 ,s_2 )$ being equal to $(1,1/2),(3/2,1/2)$ and $(3/2,1)$; all of them have very similar properties. The ground state is found to be ferrimagnetic with total spin $s_G =N(s_1 - s_2)$. We find that there is a gapless excitation to a state with spin $s_G -1$, and a gapped excitation to a state with spin $s_G +1$. Surprisingly, the correlation length in the ground state is found to be very small for this gapless system. The DMRG analysis shows that the chain is susceptible to a conditional spin-Peierls instability. Furthermore, our studies of the magnetization, magnetic susceptibility $\chi$ and specific heat show strong magnetic-field dependences. The product $\chi T$ shows a minimum as a function of temperature T at low magnetic fields; the minimum vanishes at high magnetic fields. This low-field behavior is in agreement with earlier experimental observations. The specific heat shows a maximum as a function of temperature, and the height of the maximum increases sharply at high magnetic fields. Although all the three systems show qualitatively similar behavior, there are some notable quantitative differences between the systems in which the site spin difference, $|s_1 - s_2|$, is large and small respectively.Comment: 16 LaTeX pages, 13 postscript figure

Anisotropy effects in a mixed quantum-classical Heisenberg model in two dimensions

We analyse a specific two dimensional mixed spin Heisenberg model with exchange anisotropy, by means of high temperature expansions and Monte Carlo simulations. The goal is to describe the magnetic properties of the compound (NBu_{4})_{2}Mn_{2}[Cu(opba)]_{3}\cdot 6DMSO\cdot H_{2}O which exhibits a ferromagnetic transition at $T_{c}=15K$. Extrapolating our analysis on the basis of renormalisation group arguments, we find that this transition may result from a very weak anisotropy effect.Comment: 8 pages, 10 Postscript figure

Matrix product states approach to the Heisenberg ferrimagnetic spin chains

We propose a new version of the matrix product (MP) states approach to the description of quantum spin chains, which allows one to construct MP states with certain total spin and its z-projection. We show that previously known MP wavefunctions for integer-spin antiferromagnetic chains and ladders correspond to some particular cases of our general ansatz. Our method allows to describe systems with spontaneously broken rotational symmetry, like quantum ferrimagnetic chains whose ground state has nonzero total spin. We apply this approach to describe the ground state properties of the isotropic ferrimagnetic Heisenberg chain with alternating spins 1 and 1/2 and compare our variational results with the high-precision numerical data obtained by means of the quantum Monte Carlo (QMC) method. For both the ground state energy and the correlation functions we obtain very good agreement between the variational results and the QMC data.Comment: 4 pages, RevTeX, uses psfig.sty, submitted to Phys. Rev.

Magnetic Properties of J-J-J' Quantum Heisenberg Chains with Spin S=1/2, 1, 3/2 and 2 in a Magnetic Field

By means of the density matrix renormalization group (DMRG) method, the magnetic properties of the J-J-J$^{\prime}$ quantum Heisenberg chains with spin $S=1/2$, 1, 3/2 and 2 in the ground states are investigated in the presence of a magnetic field. Two different cases are considered: (a) when $J$ is antiferromagnetic and $J^{\prime}$ is ferromagnetic (i.e. the AF-AF-F chain), the system is a ferrimagnet. The plateaus of the magnetization are observed. It is found that the width of the plateaus decreases with increasing the ferromagnetic coupling, and disappears when $$ passes over a critical value. The saturated field is observed to be independent of the ferromagnetic coupling; (b) when $J$ is ferromagnetic and $J^{\prime}$ is antiferromagnetic (i.e. the F-F-AF chain), the system becomes an antiferromagnet. The plateaus of the magnetization are also seen. The width of the plateaus decreases with decreasing the antiferromagnetic coupling, and disappears when $J^{\prime}/J$ passes over a critical value. Though the ground state properties are quite different, the magnetization plateaus in both cases tend to disappear when the ferromagnetic coupling becomes more dominant. Besides, no fundamental difference between the systems with spin half-integer and integer has been found.Comment: 8 pages, 9 figures, to be published in J. Phys.: Condens. Matte

Spin and exchange coupling for Ti embedded in a surface dipolar network

We have studied the spin and exchange coupling of Ti atoms on a Cu$_2$N/Cu(100) surface using density functional theory. We find that individual Ti have a spin of 1.0 (i.e., 2 Bohr Magneton) on the Cu$_2$N/Cu(100) surface instead of spin-1/2 as found by Scanning Tunneling Microscope. We suggest an explanation for this difference, a two-stage Kondo effect, which can be verified by experiments. By calculating the exchange coupling for Ti dimers on the Cu$_2$N/Cu(100) surface, we find that the exchange coupling across a `void' of 3.6\AA\ is antiferromagnetic, whereas indirect (superexchange) coupling through a N atom is ferromagnetic. We confirm the existence of superexchange interactions by varying the Ti-N angle in a model trimer calculation. For a square lattice of Ti on Cu$_2$N/Cu(100), we find a novel spin striped phase