6,383 research outputs found
Defect energy of infinite-component vector spin glasses
We compute numerically the zero temperature defect energy, Delta E, of the
vector spin glass in the limit of an infinite number of spin components m, for
a range of dimensions 2 <= d <= 5. Fitting to Delta E ~ L^theta, where L is the
system size, we obtain: theta = -1.54 (d=2), theta = -1.04 (d=3), theta = -0.67
(d=4) and theta = -0.37 (d=5). These results show that the lower critical
dimension, d_l (the dimension where theta changes sign), is significantly
higher for m=infinity than for finite m (where 2 < d_l < 3).Comment: 4 pages, 5 figure
Spin glasses in the limit of an infinite number of spin components
We consider the spin glass model in which the number of spin components, m,
is infinite. In the formulation of the problem appropriate for numerical
calculations proposed by several authors, we show that the order parameter
defined by the long-distance limit of the correlation functions is actually
zero and there is only "quasi long range order" below the transition
temperature. We also show that the spin glass transition temperature is zero in
three dimensions.Comment: 9 pages, 13 figure
Evidence for existence of many pure ground states in 3d Spin Glasses
Ground states of 3d EA Ising spin glasses are calculated for sizes up to
using a combination of genetic algorithms and cluster-exact
approximation . The distribution of overlaps is calculated. For
increasing size the width of converges to a nonzero value, indicating
that many pure ground states exist for short range Ising spin glasses.Comment: 4 pages, 3 figures, 2 tables, 16 reference
On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents
Finite-size scaling (FSS) is a standard technique for measuring scaling
exponents in spin glasses. Here we present a critique of this approach,
emphasizing the need for all length scales to be large compared to microscopic
scales. In particular we show that the replacement, in FSS analyses, of the
correlation length by its asymptotic scaling form can lead to apparently good
scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page
Evidence for the droplet/scaling picture of spin glasses
We have studied the Parisi overlap distribution for the three dimensional
Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T
around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the
full Parisi replica symmetry breaking, just as was also observed in recent
Monte Carlo simulations on a cubic lattice. However, for lower temperatures our
data agree with predictions from the droplet or scaling picture. The failure to
see droplet model behaviour in Monte Carlo simulations is due to the fact that
all existing simulations have been done at temperatures too close to the
transition temperature so that sytem sizes larger than the correlation length
have not been achieved.Comment: 4 pages, 6 figure
Low-Temperature Excitations of Dilute Lattice Spin Glasses
A new approach to exploring low-temperature excitations in finite-dimensional
lattice spin glasses is proposed. By focusing on bond-diluted lattices just
above the percolation threshold, large system sizes can be obtained which
lead to enhanced scaling regimes and more accurate exponents. Furthermore, this
method in principle remains practical for any dimension, yielding exponents
that so far have been elusive. This approach is demonstrated by determining the
stiffness exponent for dimensions , (the upper critical dimension),
and . Key is the application of an exact reduction algorithm, which
eliminates a large fraction of spins, so that the reduced lattices never exceed
variables for sizes as large as L=30 in , L=9 in , or L=8
in . Finite size scaling analysis gives for ,
significantly improving on previous work. The results for and ,
and , are entirely new and are compared with
mean-field predictions made for d>=6.Comment: 7 pages, LaTex, 7 ps-figures included, added result for stiffness in
d=7, as to appear in Europhysics Letters (see
http://www.physics.emory.edu/faculty/boettcher/ for related information
The Stability of the Replica Symmetric State in Finite Dimensional Spin Glasses
According to the droplet picture of spin glasses, the low-temperature phase
of spin glasses should be replica symmetric. However, analysis of the stability
of this state suggested that it was unstable and this instability lends support
to the Parisi replica symmetry breaking picture of spin glasses. The
finite-size scaling functions in the critical region of spin glasses below T_c
in dimensions greater than 6 can be determined and for them the replica
symmetric solution is unstable order by order in perturbation theory.
Nevertheless the exact solution can be shown to be replica-symmetric. It is
suggested that a similar mechanism might apply in the low-temperature phase of
spin glasses in less than six dimensions, but that a replica symmetry broken
state might exist in more than six dimensions.Comment: 5 pages. Modified to include a paragraph on the relation of this work
to that of Newman and Stei
Finite-Size Scaling of the Domain Wall Entropy Distributions for the 2D Ising Spin Glass
The statistics of domain walls for ground states of the 2D Ising spin glass
with +1 and -1 bonds are studied for square lattices with , and = 0.5, where is the fraction of negative bonds, using periodic
and/or antiperiodic boundary conditions. When is even, almost all domain
walls have energy = 0 or 4. When is odd, most domain walls have
= 2. The probability distribution of the entropy, , is found
to depend strongly on . When , the probability distribution
of is approximately exponential. The variance of this distribution
is proportional to , in agreement with the results of Saul and Kardar. For
the distribution of is not symmetric about zero. In
these cases the variance still appears to be linear in , but the average of
grows faster than . This suggests a one-parameter scaling
form for the -dependence of the distributions of for .Comment: 13 page
Nonequilibrium critical dynamics of ferromagnetic spin systems
We use simple models (the Ising model in one and two dimensions, and the
spherical model in arbitrary dimension) to put to the test some recent ideas on
the slow dynamics of nonequilibrium systems. In this review the focus is on the
temporal evolution of two-time quantities and on the violation of the
fluctuation-dissipation theorem, with special emphasis given to nonequilibrium
critical dynamics.Comment: 11 pages, 2 figures.Contribution to the Proceedings of the ESF SPHINX
meeting `Glassy behaviour of kinetically constrained models' (Barcelona,
March 22-25, 2001). To appear in a special issue of J. Phys. Cond. Mat
Colloidal gelation and non-ergodicity transitions
Within the framework of the mode coupling theory (MCT) of structural
relaxation, mechanisms and properties of non-ergodicity transitions in rather
dilute suspensions of colloidal particles characterized by strong short-ranged
attractions are studied. Results building on the virial expansion for particles
with hard cores and interacting via an attractive square well potential are
presented, and their relevance to colloidal gelation is discussed.Comment: 10 pages, 4 figures; Talk at the Conference: "Unifying Concepts in
Glass Physics" ICTP Trieste, September 1999; to be published in J. Phys.:
Condens. Matte
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