187 research outputs found
Lamellar order, microphase structures and glassy phase in a field theoretic model for charged colloids
In this paper we present a detailed analytical study of the phase diagram and
of the structural properties of a field theoretic model with a short-range
attraction and a competing long-range screened repulsion. We provide a full
derivation and expanded discussion and digression on results previously
reported briefly in M. Tarzia and A. Coniglio, Phys. Rev. Lett. 96, 075702
(2006). The model contains the essential features of the effective interaction
potential among charged colloids in polymeric solutions. We employ the
self-consistent Hartree approximation and a replica approach, and we show that
varying the parameters of the repulsive potential and the temperature yields a
phase coexistence, a lamellar and a glassy phase. Our results suggest that the
cluster phase observed in charged colloids might be the signature of an
underlying equilibrium lamellar phase, hidden on experimental time scales, and
emphasize that the formation of microphase structures may play a prominent role
in the process of colloidal gelation.Comment: 16 pages, 7 figure
Anderson model on Bethe lattices: density of states, localization properties and isolated eigenvalue
We revisit the Anderson localization problem on Bethe lattices, putting in
contact various aspects which have been previously only discussed separately.
For the case of connectivity 3 we compute by the cavity method the density of
states and the evolution of the mobility edge with disorder. Furthermore, we
show that below a certain critical value of the disorder the smallest
eigenvalue remains delocalized and separated by all the others (localized) ones
by a gap. We also study the evolution of the mobility edge at the center of the
band with the connectivity, and discuss the large connectivity limit.Comment: 13 pages, 4 figures, Proceedings of the YKIS2009 conference,
references adde
Nonmonotonic crossover and scaling behaviors in a disordered 1D quasicrystal
We consider a noninteracting disordered 1D quasicrystal in the weak disorder
regime. We show that the critical states of the pure model approach strong
localization in strikingly different ways, depending on their renormalization
properties. A finite size scaling analysis of the inverse participation ratios
of states (IPR) of the quasicrystal shows that they are described by several
kinds of scaling functions. While most states show a progressively increasing
IPR as a function of the scaling variable, other states exhibit a nonmonotonic
`re-entrant' behavior wherein the IPR first decreases, and passes through a
minimum, before increasing. This surprising behavior is explained in the
framework of perturbation renormalization group treatment, where wavefunctions
can be computed analytically as a function of the hopping amplitude ratio and
the disorder, however it is not specific to this model. Our results should help
to clarify results of recent studies of localization due to random and
quasiperiodic potentials.Comment: Revised and expanded text (10 pages, 9 figs) as accepted for
publication in Phys Rev
Renormalization group analysis of the random first order transition
We consider the approach describing glass formation in liquids as a
progressive trapping in an exponentially large number of metastable states. To
go beyond the mean-field setting, we provide a real-space renormalization group
(RG) analysis of the associated replica free-energy functional. The present
approximation yields in finite dimensions an ideal glass transition similar to
that found in mean field. However, we find that along the RG flow the
properties associated with metastable glassy states, such as the
configurational entropy, are only defined up to a characteristic length scale
that diverges as one approaches the ideal glass transition. The critical
exponents characterizing the vicinity of the transition are the usual ones
associated with a first-order discontinuity fixed point.Comment: 5 pages, 3 figure
On the solution of a `solvable' model of an ideal glass of hard spheres displaying a jamming transition
We discuss the analytical solution through the cavity method of a mean field
model that displays at the same time an ideal glass transition and a set of
jamming points. We establish the equations describing this system, and we
discuss some approximate analytical solutions and a numerical strategy to solve
them exactly. We compare these methods and we get insight into the reliability
of the theory for the description of finite dimensional hard spheres.Comment: 31 pages, 8 figure
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