663 research outputs found
Glass models on Bethe lattices
We consider ``lattice glass models'' in which each site can be occupied by at
most one particle, and any particle may have at most l occupied nearest
neighbors. Using the cavity method for locally tree-like lattices, we derive
the phase diagram, with a particular focus on the vitreous phase and the
highest packing limit. We also study the energy landscape via the
configurational entropy, and discuss different equilibrium glassy phases.
Finally, we show that a kinetic freezing, depending on the particular dynamical
rules chosen for the model, can prevent the equilibrium glass transitions.Comment: 24 pages, 11 figures; minor corrections + enlarged introduction and
conclusio
Random Vibrational Networks and Renormalization Group
We consider the properties of vibrational dynamics on random networks, with
random masses and spring constants. The localization properties of the
eigenstates contrast greatly with the Laplacian case on these networks. We
introduce several real-space renormalization techniques which can be used to
describe this dynamics on general networks, drawing on strong disorder
techniques developed for regular lattices. The renormalization group is capable
of elucidating the localization properties, and provides, even for specific
network instances, a fast approximation technique for determining the spectra
which compares well with exact results.Comment: 4 pages, 3 figure
Do current-density nonlinearities cut off the glass transition?
Extended mode coupling theories for dense fluids predict that nonlinear
current-density couplings cut off the singular `ideal glass transition',
present in the standard mode coupling theory where such couplings are ignored.
We suggest here that, rather than allowing for activated processes as sometimes
supposed, contributions from current-density couplings are always negligible
close to a glass transition. We discuss in schematic terms how activated
processes can nonetheless cut off the transition, by causing the memory
function to become linear in correlators at late times.Comment: 4 page
Expansion of the Gibbs potential for quantum many-body systems: General formalism with applications to the spin glass and the weakly non-ideal Bose gas
For general quantum systems the power expansion of the Gibbs potential and
consequently the power expansion of the self energy is derived in terms of the
interaction strength. Employing a generalization of the projector technique a
compact representation of the general terms of the expansion results. The
general aspects of the approach are discussed with special emphasis on the
effects characteristic for quantum systems. The expansion is systematic and
leads directly to contributions beyond mean-field of all thermodynamic
quantities. These features are explicitly demonstrated and illustrated for two
non-trivial systems, the infinite range quantum spin glass and the weakly
interacting Bose gas. The Onsager terms of both systems are calculated, which
represent the first beyond mean-field contributions. For the spin glass new
TAP-like equations are presented and discussed in the paramagnetic region. The
investigation of the Bose gas leads to a beyond mean-field thermodynamic
description. At the Bose-Einstein condensation temperature complete agreement
is found with the results presented recently by alternative techniques.Comment: 17 pages, 0 figures; revised version accepted by Phys Rev
Spectral Density of Sparse Sample Covariance Matrices
Applying the replica method of statistical mechanics, we evaluate the
eigenvalue density of the large random matrix (sample covariance matrix) of the
form , where is an real sparse random matrix.
The difference from a dense random matrix is the most significant in the tail
region of the spectrum. We compare the results of several approximation
schemes, focusing on the behavior in the tail region.Comment: 22 pages, 4 figures, minor corrections mad
The Valence Bond Glass phase
We show that a new glassy phase can emerge in presence of strong magnetic
frustration and quantum fluctuations. It is a Valence Bond Glass. We study its
properties solving the Hubbard-Heisenberg model on a Bethe lattice within the
large limit introduced by Affleck and Marston. We work out the phase
diagram that contains Fermi liquid, dimer and valence bond glass phases. This
new glassy phase has no electronic or spin gap (although a pseudo-gap is
observed), it is characterized by long-range critical valence bond correlations
and is not related to any magnetic ordering. As a consequence it is quite
different from both valence bond crystals and spin glasses
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