2,136 research outputs found
Critical behavior of the random-anisotropy model in the strong-anisotropy limit
We investigate the nature of the critical behavior of the random-anisotropy
Heisenberg model (RAM), which describes a magnetic system with random uniaxial
single-site anisotropy, such as some amorphous alloys of rare earths and
transition metals. In particular, we consider the strong-anisotropy limit
(SRAM), in which the Hamiltonian can be rewritten as the one of an Ising
spin-glass model with correlated bond disorder. We perform Monte Carlo
simulations of the SRAM on simple cubic L^3 lattices, up to L=30, measuring
correlation functions of the replica-replica overlap, which is the order
parameter at a glass transition. The corresponding results show critical
behavior and finite-size scaling. They provide evidence of a finite-temperature
continuous transition with critical exponents and
. These results are close to the corresponding estimates that
have been obtained in the usual Ising spin-glass model with uncorrelated bond
disorder, suggesting that the two models belong to the same universality class.
We also determine the leading correction-to-scaling exponent finding .Comment: 24 pages, 13 figs, J. Stat. Mech. in pres
Energy exponents and corrections to scaling in Ising spin glasses
We study the probability distribution P(E) of the ground state energy E in
various Ising spin glasses. In most models, P(E) seems to become Gaussian with
a variance growing as the system's volume V. Exceptions include the
Sherrington-Kirkpatrick model (where the variance grows more slowly, perhaps as
the square root of the volume), and mean field diluted spin glasses having +/-J
couplings. We also find that the corrections to the extensive part of the
disorder averaged energy grow as a power of the system size; for finite
dimensional lattices, this exponent is equal, within numerical precision, to
the domain-wall exponent theta_DW. We also show how a systematic expansion of
theta_DW in powers of exp(-d) can be obtained for Migdal-Kadanoff lattices.
Some physical arguments are given to rationalize our findings.Comment: 12 pages, RevTex, 9 figure
How to compute the thermodynamics of a glass using a cloned liquid
The recently proposed strategy for studying the equilibrium thermodynamics of
the glass phase using a molecular liquid is reviewed and tested in details on
the solvable case of the -spin model. We derive the general phase diagram,
and confirm the validity of this procedure. We point out the efficacy of a
system of two weakly coupled copies in order to identify the glass transition,
and the necessity to study a system with copies ('clones') of the
original problem in order to derive the thermodynamic properties of the glass
phase.Comment: Latex, 17 pages, 6 figure
The nature of the different zero-temperature phases in discrete two-dimensional spin glasses: Entropy, universality, chaos and cascades in the renormalization group flow
The properties of discrete two-dimensional spin glasses depend strongly on
the way the zero-temperature limit is taken. We discuss this phenomenon in the
context of the Migdal-Kadanoff renormalization group. We see, in particular,
how these properties are connected with the presence of a cascade of fixed
points in the renormalization group flow. Of particular interest are two
unstable fixed points that correspond to two different spin-glass phases at
zero temperature. We discuss how these phenomena are related with the presence
of entropy fluctuations and temperature chaos, and universality in this model.Comment: 14 pages, 5 figures, 2 table
Universality-class dependence of energy distributions in spin glasses
We study the probability distribution function of the ground-state energies
of the disordered one-dimensional Ising spin chain with power-law interactions
using a combination of parallel tempering Monte Carlo and branch, cut, and
price algorithms. By tuning the exponent of the power-law interactions we are
able to scan several universality classes. Our results suggest that mean-field
models have a non-Gaussian limiting distribution of the ground-state energies,
whereas non-mean-field models have a Gaussian limiting distribution. We compare
the results of the disordered one-dimensional Ising chain to results for a
disordered two-leg ladder, for which large system sizes can be studied, and
find a qualitative agreement between the disordered one-dimensional Ising chain
in the short-range universality class and the disordered two-leg ladder. We
show that the mean and the standard deviation of the ground-state energy
distributions scale with a power of the system size. In the mean-field
universality class the skewness does not follow a power-law behavior and
converges to a nonzero constant value. The data for the Sherrington-Kirkpatrick
model seem to be acceptably well fitted by a modified Gumbel distribution.
Finally, we discuss the distribution of the internal energy of the
Sherrington-Kirkpatrick model at finite temperatures and show that it behaves
similar to the ground-state energy of the system if the temperature is smaller
than the critical temperature.Comment: 15 pages, 20 figures, 1 tabl
Functional Renormalization for Disordered Systems, Basic Recipes and Gourmet Dishes
We give a pedagogical introduction into the functional renormalization group
treatment of disordered systems. After a review of its phenomenology, we show
why in the context of disordered systems a functional renormalization group
treatment is necessary, contrary to pure systems, where renormalization of a
single coupling constant is sufficient. This leads to a disorder distribution,
which after a finite renormalization becomes non-analytic, thus overcoming the
predictions of the seemingly exact dimensional reduction. We discuss, how the
non-analyticity can be measured in a simulation or experiment. We then
construct a renormalizable field theory beyond leading order. We discuss an
elastic manifold embedded in N dimensions, and give the exact solution for N to
infinity. This is compared to predictions of the Gaussian replica variational
ansatz, using replica symmetry breaking. We further consider random field
magnets, and supersymmetry. We finally discuss depinning, both isotropic and
anisotropic, and universal scaling function.Comment: 29 page
Thermodynamics and Universality for Mean Field Quantum Spin Glasses
We study aspects of the thermodynamics of quantum versions of spin glasses.
By means of the Lie-Trotter formula for exponential sums of operators, we adapt
methods used to analyze classical spin glass models to answer analogous
questions about quantum models.Comment: 17 page
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