8,392 research outputs found
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 , the upper
invariant measure has the following property: Conditioned on the event that
is infected, the events All sites are healthy and All
sites 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
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 and alternating from site to site and
interacting via a Heisenberg antiferromagnetic exchange. The three systems
studied correspond to being equal to and
; all of them have very similar properties. The ground state is found
to be ferrimagnetic with total spin . We find that there is
a gapless excitation to a state with spin , and a gapped excitation to
a state with spin . 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
and specific heat show strong magnetic-field dependences. The product
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, , 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 . 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
Ocean tides and quasi-stationary departures from the marine geoid investigation
The detection of tides and/or currents through the analysis of data generated in connection with the Ocean Geoid Determination Investigation is presented. A discussion of the detailed objectives and approach are included
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 phase diagram of a frustrated ferrimagnetic ladder: Relation to the one-dimensional boson Hubbard model
We study the magnetic phase diagram of two coupled mixed-spin
Heisenberg chains as a function of the frustration parameter related to
diagonal exchange couplings. The analysis is performed by using spin-wave
series and exact numerical diagonalization techniques. The obtained phase
diagram--containing the Luttinger liquid phase, the plateau phase with a
magnetization per rung , and the fully polarized phase--is closely
related to the generic phase diagram of the one-dimensional boson
Hubbard model.Comment: 4 pages, 2 figure
Phase diagram of a frustrated mixed-spin ladder with diagonal exchange bonds
Using exact numerical diagonalization and the conformal field theory
approach, we study the effect of magnetic frustrations due to diagonal exchange
bonds in a system of two coupled mixed-spin Heisenberg chains. It
is established that relatively moderate frustrations are able to destroy the
ferrimagnetic state and to stabilize the critical spin-liquid phase typical for
half-integer-spin antiferromagnetic Heisenberg chains. Both phases are
separated by a narrow but finite region occupied by a critical
partially-polarized ferromagnetic phase.Comment: 5 PRB pages, 7 eps figures, to appear in Phys. Rev.
Some conditional correlation inequalities for percolation and related processes
Consider ordinary bond percolation on a finite or countably infinite graph. Let s, t, a and b be vertices. An earlier paper proved the (nonintuitive) result that, conditioned on the event that there is no open path from s to t, the two events ``there is an open path from s to a' and ``there is an open path from s to b' are positively correlated. In the present paper we further investigate and generalize the theorem of which this result was a consequence. This leads to results saying, informally, that, with the above conditioning, the open cluster of s is conditionally positively (self-)associated and that it is conditionally negatively correlated with the open cluster of t. We also present analogues of some of our results for (a) random-cluster measures, and (b) directed percolation and contact processes, and observe that the latter lead to improvements of some of the results in a paper of Belitsky, Ferrari, Konno and Liggett (1997
Gravity anomaly detection: Apollo/Soyuz
The Goddard Apollo-Soyuz Geodynamics Experiment is described. It was performed to demonstrate the feasibility of tracking and recovering high frequency components of the earth's gravity field by utilizing a synchronous orbiting tracking station such as ATS-6. Gravity anomalies of 5 MGLS or larger having wavelengths of 300 to 1000 kilometers on the earth's surface are important for geologic studies of the upper layers of the earth's crust. Short wavelength Earth's gravity anomalies were detected from space. Two prime areas of data collection were selected for the experiment: (1) the center of the African continent and (2) the Indian Ocean Depression centered at 5% north latitude and 75% east longitude. Preliminary results show that the detectability objective of the experiment was met in both areas as well as at several additional anomalous areas around the globe. Gravity anomalies of the Karakoram and Himalayan mountain ranges, ocean trenches, as well as the Diamantina Depth, can be seen. Maps outlining the anomalies discovered are shown
Electronic structure of the molecule based magnet Cu PM(NO3)2 (H2O)2
We present density functional calculations on the molecule based S=1/2
antiferromagnetic chain compound Cu PM(NO3)2 (H2O)2; PM = pyrimidine. The
properties of the ferro- and antiferromagnetic state are investigated at the
level of the local density approximation and with the hybrid functional B3LYP.
Spin density maps illustrate the exchange path via the pyrimidine molecule
which mediates the magnetism in the one-dimensional chain. The computed
exchange coupling is antiferromagnetic and in reasonable agreement with the
experiment. It is suggested that the antiferromagnetic coupling is due to the
possibility of stronger delocalization of the charges on the nitrogen atoms,
compared to the ferromagnetic case. In addition, computed isotropic and
anisotropic hyperfine interaction parameters are compared with recent NMR
experiments
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