4,780 research outputs found
The ideal glass transition of Hard Spheres
We use the replica method to study the ideal glass transition of a liquid of
identical Hard Spheres. We obtain estimates of the configurational entropy in
the liquid phase, of the Kauzmann packing fraction, in the range 0.58--0.62,
and of the random close packing density, in the range 0.64--0.67, depending on
the approximation we use for the equation of state of the liquid. We also
compute the pair correlation function in the glassy states (i.e., dense
amorphous packings) and we find that the mean coordination number at random
close packing is equal to 6. All these results compare well with numerical
simulations and with other existing theories.Comment: 13 pages, 8 figure
Amorphous packings of hard spheres in large space dimension
In a recent paper (cond-mat/0506445) we derived an expression for the
replicated free energy of a liquid of hard spheres based on the HNC free energy
functional. An approximate equation of state for the glass and an estimate of
the random close packing density were obtained in d=3. Here we show that the
HNC approximation is not needed: the same expression can be obtained from the
full diagrammatic expansion of the replicated free energy. Then, we consider
the asymptotics of this expression when the space dimension d is very large. In
this limit, the entropy of the hard sphere liquid has been computed exactly.
Using this solution, we derive asymptotic expressions for the glass transition
density and for the random close packing density for hard spheres in large
space dimension.Comment: 11 pages, 1 figure, includes feynmf diagram
Fragility in p-spin models
We investigate the relation between fragility and phase space properties -
such as the distribution of states - in the mean field p-spin model, a solvable
model that has been frequently used in studies of the glass transition. By
direct computation of all the relevant quantities, we find that: i) the
recently observed correlation between fragility and vibrational properties at
low temperature is present in this model; ii) the total number of states is a
decreasing function of fragility, at variance of what is currently believed. We
explain these findings by taking into account the contribution to fragility
coming from the transition paths between different states. Finally, we propose
a geometric picture of the phase space that explains the correlation between
properties of the transition paths, distribution of states and their
vibrational properties. However, our analysis may not apply to strong systems
where inflection points in the configurational entropy as a function of the
temperature are found
Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation
We study systems without quenched disorder with a complex landscape, and we
use replica symmetry theory to describe them. We discuss the
Golay-Bernasconi-Derrida approximation of the low autocorrelation model, and we
reconstruct it by using replica calculations. Then we consider the full model,
its low properties (with the help of number theory) and a Hartree-Fock
resummation of the high-temperature series. We show that replica theory allows
to solve the model in the high phase. Our solution is based on one-link
integral techniques, and is based on substituting a Fourier transform with a
generic unitary transformation. We discuss this approach as a powerful tool to
describe systems with a complex landscape in the absence of quenched disorder.Comment: 42 pages, uufile with eps figures added in figures, ROM2F/94/1
Spin-1 gravitational waves. Theoretical and experimental aspects
Exact solutions of Einstein field equations invariant for a non-Abelian
2-dimensional Lie algebra of Killing fields are described. Physical properties
of these gravitational fields are studied, their wave character is checked by
making use of covariant criteria and the observable effects of such waves are
outlined. The possibility of detection of these waves with modern detectors,
spherical resonant antennas in particular, is sketched
On the origin of ultrametricity
In this paper we show that in systems where the probability distribution of
the the overlap is non trivial in the infinity volume limit, the property of
ultrametricity can be proved in general starting from two very simple and
natural assumptions: each replica is equivalent to the others (replica
equivalence or stochastic stability) and all the mutual information about a
pair of equilibrium configurations is encoded in their mutual distance or
overlap (separability or overlap equivalence).Comment: 13 pages, 1 figur
A note on rattlers in amorphous packings of binary mixtures of hard spheres
It has been recently pointed out by Farr and Groot (arXiv:0912.0852) and by
Kyrylyuk and Philipse (Prog. Colloid Polym. Sci., 2010, in press) that our
theoretical result for the jamming density of a binary mixture of hard spheres
(arXiv:0903.5099) apparently violates an upper bound that is obtained by
considering the limit where the diameter ratio r = DA/DB goes to infinity. We
believe that this apparent contradiction is the consequence of a
misunderstanding, which we try to clarify here.Comment: 2 pages, 2 figures; final version published on J.Chem.Phy
On the Use of Optimized Monte Carlo Methods for Studying Spin Glasses
We start from recently published numerical data by Hatano and Gubernatis
cond-mat/0008115 to discuss properties of convergence to equilibrium of
optimized Monte Carlo methods (bivariate multi canonical and parallel
tempering). We show that these data are not thermalized, and they lead to an
erroneous physical picture. We shed some light on why the bivariate multi
canonical Monte Carlo method can fail.Comment: 6 pages, 5 eps figures include
Explicit generation of the branching tree of states in spin glasses
We present a numerical method to generate explicit realizations of the tree
of states in mean-field spin glasses. The resulting study illuminates the
physical meaning of the full replica symmetry breaking solution and provides
detailed information on the structure of the spin-glass phase. A cavity
approach ensures that the method is self-consistent and permits the evaluation
of sophisticated observables, such as correlation functions. We include an
example application to the study of finite-size effects in single-sample
overlap probability distributions, a topic that has attracted considerable
interest recently.Comment: Version accepted for publication in JSTA
On the Use of Optimized Monte Carlo Methods for Studying Spin Glasses
We start from recently published numerical data by Hatano and Gubernatis
cond-mat/0008115 to discuss properties of convergence to equilibrium of
optimized Monte Carlo methods (bivariate multi canonical and parallel
tempering). We show that these data are not thermalized, and they lead to an
erroneous physical picture. We shed some light on why the bivariate multi
canonical Monte Carlo method can fail.Comment: 6 pages, 5 eps figures include
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