1,066 research outputs found
Direct sampling of complex landscapes at low temperatures: the three-dimensional +/-J Ising spin glass
A method is presented, which allows to sample directly low-temperature
configurations of glassy systems, like spin glasses. The basic idea is to
generate ground states and low lying excited configurations using a heuristic
algorithm. Then, with the help of microcanonical Monte Carlo simulations, more
configurations are found, clusters of configurations are determined and
entropies evaluated. Finally equilibrium configuration are randomly sampled
with proper Gibbs-Boltzmann weights.
The method is applied to three-dimensional Ising spin glasses with +- J
interactions and temperatures T<=0.5. The low-temperature behavior of this
model is characterized by evaluating different overlap quantities, exhibiting a
complex low-energy landscape for T>0, while the T=0 behavior appears to be less
complex.Comment: 9 pages, 7 figures, revtex (one sentence changed compared to v2
Spin Models on Thin Graphs
We discuss the utility of analytical and numerical investigation of spin
models, in particular spin glasses, on ordinary ``thin'' random graphs (in
effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two
dimensional gravity. We highlight the similarity with Bethe lattice
calculations and the advantages of the thin graph approach both analytically
and numerically for investigating mean field results.Comment: Contribution to Parallel Session at Lattice95, 4 pages. Dodgy
compressed ps file replaced with uuencoded LaTex original + ps figure
SrCu_2(BO_3)_2 - a Two Dimensional Spin Liquid
We study an extended Shastry-Sutherland model for SrCu_2(BO_3)_2 and analyze
the low lying parts of the energy spectrum by means of a perturbative unitary
transformation based on flow equations. The derivation of the 1-magnon
dispersion (elementary triplets) is discussed. Additionally, we give a
quantitative description (symmetries and energies) of bound states made from
two elementary triplets. Our high order results allow to fix the model
parameters for SrCu_2(BO_3)_2 precisely: J_1=6.16(10)meV, x:=J_2/J_1=0.603(3),
J_\perp=1.3(2)meV. To our knowledge this is the first quantitative treatment of
bound states in a true 2d model.Comment: 4 pages, 3 figures, Proceeding paper of the HFM2000 conference in
Waterloo, Canada, Jun 200
Dislocation-induced spin tunneling in Mn-12 acetate
Comprehensive theory of quantum spin relaxation in Mn-12 acetate crystals is
developed, that takes into account imperfections of the crystal structure and
is based upon the generalization of the Landau-Zener effect for incoherent
tunneling from excited energy levels. It is shown that linear dislocations at
plausible concentrations provide the transverse anisotropy which is the main
source of tunneling in Mn-12. Local rotations of the easy axis due to
dislocations result in a transverse magnetic field generated by the field
applied along the c-axis of the crystal, which explains the presence of odd
tunneling resonances. Long-range deformations due to dislocations produce a
broad distribution of tunnel splittings. The theory predicts that at subkelvin
temperatures the relaxation curves for different tunneling resonances can be
scaled onto a single master curve. The magnetic relaxation in the thermally
activated regime follows the stretched-exponential law with the exponent
depending on the field, temperature, and concentration of defects.Comment: 17 pages, 14 figures, 1 table, submitted to PR
Tunneling with dissipation and decoherence for a large spin
We present rigorous solution of problems of tunneling with dissipation and
decoherence for a spin of an atom or a molecule in an isotropic solid matrix.
Our approach is based upon switching to a rotating coordinate system coupled to
the local crystal field. We show that the spin of a molecule can be used in a
qubit only if the molecule is strongly coupled with its atomic environment.
This condition is a consequence of the conservation of the total angular
momentum (spin + matrix), that has been largely ignored in previous studies of
spin tunneling.Comment: 4 page
The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
The nature of the zero temperature ordering transition in the 3D Gaussian
random field Ising magnet is studied numerically, aided by scaling analyses. In
the ferromagnetic phase the scaling of the roughness of the domain walls,
, is consistent with the theoretical prediction .
As the randomness is increased through the transition, the probability
distribution of the interfacial tension of domain walls scales as for a single
second order transition. At the critical point, the fractal dimensions of
domain walls and the fractal dimension of the outer surface of spin clusters
are investigated: there are at least two distinct physically important fractal
dimensions. These dimensions are argued to be related to combinations of the
energy scaling exponent, , which determines the violation of
hyperscaling, the correlation length exponent , and the magnetization
exponent . The value is derived from the
magnetization: this estimate is supported by the study of the spin cluster size
distribution at criticality. The variation of configurations in the interior of
a sample with boundary conditions is consistent with the hypothesis that there
is a single transition separating the disordered phase with one ground state
from the ordered phase with two ground states. The array of results are shown
to be consistent with a scaling picture and a geometric description of the
influence of boundary conditions on the spins. The details of the algorithm
used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure
On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers
We present an efficient quantum algorithm for the exact evaluation of either
the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function
Z for a family of graphs related to irreducible cyclic codes. This problem is
related to the evaluation of the Jones and Tutte polynomials. We consider the
connection between the weight enumerator polynomial from coding theory and Z
and exploit the fact that there exists a quantum algorithm for efficiently
estimating Gauss sums in order to obtain the weight enumerator for a certain
class of linear codes. In this way we demonstrate that for a certain class of
sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\epsilon)
graphs, quantum computers provide a polynomial speed up in the difference
between the number of edges and vertices of the graph, and an exponential speed
up in q, over the best classical algorithms known to date
A Sawtooth-like Timeline for the First Billion Year of Lunar Bombardment
We revisit the early evolution of the Moon's bombardment. Our work combines
modeling (based on plausible projectile sources and their dynamical decay
rates) with constraints from the lunar crater record, radiometric ages of the
youngest lunar basins, and the abundance of highly siderophile elements in the
lunar crust and mantle. We deduce that the evolution of the impact flux did not
decline exponentially over the first billion years of lunar history, but also
there was no prominent and "narrow" impact spike some 3.9 Gy ago, unlike that
typically envisioned in the lunar cataclysm scenario. Instead, we show the
timeline of the lunar bombardment has a sawtooth-like profile, with an uptick
in the impact flux near 4.1 Gy ago. The impact flux at the beginning of this
weaker cataclysm was 5-10 times higher than the immediately preceding period.
The Nectaris basin should have been one of the first basins formed at the
sawtooth. We predict the bombardment rate since about 4.1Gy ago declined slowly
and adhered relatively close to classic crater chronology models (Neukum and
Ivanov (1994)). Overall we expect that the sawtooth event accounted for about
1/4 of the total bombardment suffered by the Moon since its formation.
Consequently, considering that about 12-14 basins formed during the sawtooth
event, we expect that the net number of basins formed on the Moon was about
45-50. From our expected bombardment timeline, we derived a new and improved
lunar chronology suitable for use on Pre-Nectarian surface units. According to
this chronology, a significant portion of the oldest lunar cratered terrains
has an age of 4.38-4.42 Gyr. Moreover, the largest lunar basin, South Pole
Aitken, is older than 4.3Gy, and therefore was not produced during the lunar
cataclysm.Comment: In press in EPS
Spin Glasses on Thin Graphs
In a recent paper we found strong evidence from simulations that the
Isingantiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed
amean-field spin glass transition. The intrinsic interest of considering such
random graphs is that they give mean field results without long range
interactions or the drawbacks, arising from boundary problems, of the Bethe
lattice. In this paper we reprise the saddle point calculations for the Ising
and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We
use standard results from bifurcation theory that enable us to treat an
arbitrary number of replicas and any quenched bond distribution. We note the
agreement between the ferromagnetic and spin glass transition temperatures thus
calculated and those derived by analogy with the Bethe lattice, or in previous
replica calculations. We then investigate numerically spin glasses with a plus
or minus J bond distribution for the Ising and Q=3,4,10,50 state Potts models,
paying particular attention to the independence of the spin glass transition
from the fraction of positive and negative bonds in the Ising case and the
qualitative form of the overlap distribution in all the models. The parallels
with infinite range spin glass models in both the analytical calculations and
simulations are pointed out.Comment: 13 pages of LaTex and 11 postscript figures bundled together with
uufiles. Discussion of first order transitions for three or more replicas
included and similarity to Ising replica magnet pointed out. Some additional
reference
Crystal and magnetic structure of LaTiO3 : evidence for non-degenerate -orbitals
The crystal and magnetic structure of LaTiO3 ~ has been studied by x-ray and
neutron diffraction techniques using nearly stoichiometric samples. We find a
strong structural anomaly near the antiferromagnetic ordering, T=146 K. In
addition, the octahedra in LaTiO3 exhibit an intrinsic distortion which implies
a splitting of the t2g-levels. Our results indicate that LaTiO3 should be
considered as a Jahn-Teller system where the structural distortion and the
resulting level splitting are enhanced by the magnetic ordering.Comment: 4 pages 5 figure
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