83 research outputs found
Partitioning of energy in highly polydisperse granular gases
A highly polydisperse granular gas is modeled by a continuous distribution of
particle sizes, a, giving rise to a corresponding continuous temperature
profile, T(a), which we compute approximately, generalizing previous results
for binary or multicomponent mixtures. If the system is driven, it evolves
towards a stationary temperature profile, which is discussed for several
driving mechanisms in dependence on the variance of the size distribution. For
a uniform distribution of sizes, the stationary temperature profile is
nonuniform with either hot small particles (constant force driving) or hot
large particles (constant velocity or constant energy driving). Polydispersity
always gives rise to non-Gaussian velocity distributions. Depending on the
driving mechanism the tails can be either overpopulated or underpopulated as
compared to the molecular gas. The deviations are mainly due to small
particles. In the case of free cooling the decay rate depends continuously on
particle size, while all partial temperatures decay according to Haff's law.
The analytical results are supported by event driven simulations for a large,
but discrete number of species.Comment: 10 pages; 5 figure
Sample-to-sample fluctuations and bond chaos in the -component spin glass
We calculate the finite size scaling of the sample-to-sample fluctuations of
the free energy of the component vector spin glass in the
large- limit. This is accomplished using a variant of the interpolating
Hamiltonian technique which is used to establish a connection between the free
energy fluctuations and bond chaos. The calculation of bond chaos then shows
that the scaling of the free energy fluctuaions with system size is with , and very likely
exactly.Comment: 12 pages, 1 figur
Why temperature chaos in spin glasses is hard to observe
The overlap length of a three-dimensional Ising spin glass on a cubic lattice
with Gaussian interactions has been estimated numerically by transfer matrix
methods and within a Migdal-Kadanoff renormalization group scheme. We find that
the overlap length is large, explaining why it has been difficult to observe
spin glass chaos in numerical simulations and experiment.Comment: 4 pages, 6 figure
Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions
The one-dimensional Ising spin-glass model with power-law long-range
interactions is a useful proxy model for studying spin glasses in higher space
dimensions and for finding the dimension at which the spin-glass state changes
from having broken replica symmetry to that of droplet behavior. To this end we
have calculated the exponent that describes the difference in free energy
between periodic and antiperiodic boundary conditions. Numerical work is done
to support some of the assumptions made in the calculations and to determine
the behavior of the interface free-energy exponent of the power law of the
interactions. Our numerical results for the interface free-energy exponent are
badly affected by finite-size problems.Comment: 10 pages, 5 figures, 3 table
Complexity in Mean-Field Spin-Glass Models: Ising -spin
The Complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising
-spin is investigated in the temperature regime where the equilibrium phase
is one step Replica Symmetry
Breaking. Two solutions of the resulting saddle point equations are found.
One is supersymmetric (SUSY) and includes the equilibrium value of the free
energy while the other is non-SUSY. The two solutions cross exactly at a value
of the free energy where the replicon eigenvalue is zero; at low free energy
the complexity is described by the SUSY solution while at high free energy it
is described by the non-SUSY solution. In particular the non-SUSY solution
describes the total number of solutions, like in the
Sherrington-Kirkpatrick (SK) model. The relevant TAP solutions corresponding
to the non-SUSY solution share the same feature of the corresponding solutions
in the SK model, in particular their Hessian has a vanishing isolated
eigenvalue. The TAP solutions corresponding to the SUSY solution, instead, are
well separated minima.Comment: 13 pages, 9 figure
Generalised Bose-Einstein phase transition in large- component spin glasses
It is proposed to understand finite dimensional spin glasses using a
expansion, where is the number of spin components. It is shown that this
approach predicts a replica symmetric state in finite dimensions. The point
about which the expansion is made, the infinite- limit, has been studied in
the mean-field limit in detail and has a very unusual phase transition, rather
similar to a Bose-Einstein phase transition but with macroscopically
occupied low-lying states.Comment: 4 pages (plus a few lines), 3 figures. v2: minor error corrected. v3:
numerics supplemented by analytical arguments, references added, figure of
density of states adde
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