28,661 research outputs found
Comment on "Evidence for nontrivial ground-state structure of 3d +/- J spin glasses"
In a recent Letter [Europhys. Lett. 40, 429 (1997)], Hartmann presented
results for the structure of the degenerate ground states of the
three-dimensional +/- J spin glass model obtained using a genetic algorithm. In
this Comment, I argue that the method does not produce the correct
thermodynamic distribution of ground states and therefore gives erroneous
results for the overlap distribution. I present results of simulated annealing
calculations using different annealing rates for cubic lattices with
N=4*4*4spins. The disorder-averaged overlap distribution exhibits a significant
dependence on the annealing rate, even when the energy has converged. For fast
annealing, moments of the distribution are similar to those presented by
Hartmann. However, as the annealing rate is lowered, they approach the results
previously obtained using a multi-canonical Monte Carlo method. This shows
explicitly that care must be taken not only to reach states with the lowest
energy but also to ensure that they obey the correct thermodynamic
distribution, i.e., that the probability is the same for reaching any of the
ground states.Comment: 2 pages, Revtex, 1 PostScript figur
Critical behavior of the Random-Field Ising model at and beyond the Upper Critical Dimension
The disorder-driven phase transition of the RFIM is observed using exact
ground-state computer simulations for hyper cubic lattices in d=5,6,7
dimensions. Finite-size scaling analyses are used to calculate the critical
point and the critical exponents of the specific heat, magnetization,
susceptibility and of the correlation length. For dimensions d=6,7 which are
larger or equal to the assumed upper critical dimension, d_u=6, mean-field
behaviour is found, i.e. alpha=0, beta=1/2, gamma=1, nu=1/2. For the analysis
of the numerical data, it appears to be necessary to include recently proposed
corrections to scaling at and beyond the upper critical dimension.Comment: 8 pages and 13 figures; A consise summary of this work can be found
in the papercore database at http://www.papercore.org/Ahrens201
Critical behavior of the Random-Field Ising Magnet with long range correlated disorder
We study the correlated-disorder driven zero-temperature phase transition of
the Random-Field Ising Magnet using exact numerical ground-state calculations
for cubic lattices. We consider correlations of the quenched disorder decaying
proportional to r^a, where r is the distance between two lattice sites and a<0.
To obtain exact ground states, we use a well established mapping to the
graph-theoretical maximum-flow problem, which allows us to study large system
sizes of more than two million spins. We use finite-size scaling analyses for
values a={-1,-2,-3,-7} to calculate the critical point and the critical
exponents characterizing the behavior of the specific heat, magnetization,
susceptibility and of the correlation length close to the critical point. We
find basically the same critical behavior as for the RFIM with delta-correlated
disorder, except for the finite-size exponent of the susceptibility and for the
case a=-1, where the results are also compatible with a phase transition at
infinitesimal disorder strength.
A summary of this work can be found at the papercore database at
www.papercore.org.Comment: 9 pages, 13 figure
Ground-state landscape of 2d +-J Ising spin glasses
Large numbers of ground states of two-dimensional Ising spin glasses with
periodic boundary conditions in both directions are calculated for sizes up to
40^2. A combination of a genetic algorithm and Cluster-Exact Approximation is
used. For each quenched realization of the bonds up to 40 independent ground
states are obtained.
For the infinite system a ground-state energy of e=-1.4015(3) is
extrapolated. The ground-state landscape is investigated using a finite-size
scaling analysis of the distribution of overlaps. The mean-field picture
assuming a complex landscape describes the situation better than the
droplet-scaling model, where for the infinite system mainly two ground states
exist. Strong evidence is found that the ground states are not organized in an
ultrametric fashion in contrast to previous results for three-dimensional spin
glasses.Comment: 9 pages, revtex, 11 figures, 51 reference
Martian Cratering 4: Mariner 9 Initial Analysis of Cratering Chronology
Early analyses of cratering and other Martian surface properties that indicated extensive ancient erosion have been strongly supported by Mariner 9 data. By their great variations in density, these craters indicate a history of Martian erosion and crustal development intermediate between earth and the moon
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