3,148 research outputs found
Phase Transitions in Granular Packings
We describe the contact network of granular packings by a frustrated lattice
gas that contains steric frustration as essential ingredient. Two transitions
are identified, a spin glass transition at the onset of Reynolds dilatancy and
at lower densities a percolation transition. We describe the correlation
functions that give rise to the singularities and propose some dynamical
experiments
Mean Field Critical Behaviour for a Fully Frustrated Blume-Emmery-Griffiths Model
We present a mean field analysis of a fully frustrated Ising spin model on an
Ising lattice gas. This is equivalent to a degenerate Blume-Emery-Griffiths
model with frustration, which we analyze for different values of the
quadrupolar interaction. This model might be useful in the study of structural
glasses and related systems with disorder
Petzval type objective including field shaping lens Patent
Development and characteristics of Petzval type objective including field shaping lens for focusing light of specified wavelength band on curved photorecepto
Percolation and Cluster Formalism in Continuous Spin Systems
The generalization of Kasteleyn and Fortuin clusters formalism is introduced
in XY (or more generally O(n)) models. Clusters geometrical structure may be
linked to spin physical properties as correlation functions. To investigate
percolative characteristics, the new cluster definition is analytically
explored in one dimension and with Monte Carlo simulations in 2D and 3D
frustrated and unfrustrated n-clock models. In these models (also in
unfrustrated cases for large n) the percolative transition temperature is
higher than the usual thermodynamical critical one.Comment: 12 pages and 4 figure
A Geometrical Interpretation of Hyperscaling Breaking in the Ising Model
In random percolation one finds that the mean field regime above the upper
critical dimension can simply be explained through the coexistence of infinite
percolating clusters at the critical point. Because of the mapping between
percolation and critical behaviour in the Ising model, one might check whether
the breakdown of hyperscaling in the Ising model can also be intepreted as due
to an infinite multiplicity of percolating Fortuin-Kasteleyn clusters at the
critical temperature T_c. Preliminary results suggest that the scenario is much
more involved than expected due to the fact that the percolation variables
behave differently on the two sides of T_c.Comment: Lattice2002(spin
A model-theoretic analysis of Fidel-structures for mbC
In this paper the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC (or mbC-structures) can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N (for negation) and O (for the consistency connective) satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theory in order to analyze the class of mbC-structures. Thus, substructures, union of chains, direct products, direct limits, congruences and quotient structures can be analyzed under this perspective. In particular, a Birkhoff-like representation theorem for mbC-structures as subdirect poducts in terms of subdirectly irreducible mbC-structures is obtained by adapting a general result for first-order structures due to Caicedo. Moreover, a characterization of all the subdirectly irreducible mbC-structures is also given. An alternative decomposition theorem is obtained by using the notions of weak substructure and weak isomorphism considered by Fidel for Cn-structures
Precursor phenomena in frustrated systems
To understand the origin of the dynamical transition, between high
temperature exponential relaxation and low temperature nonexponential
relaxation, that occurs well above the static transition in glassy systems, a
frustrated spin model, with and without disorder, is considered. The model has
two phase transitions, the lower being a standard spin glass transition (in
presence of disorder) or fully frustrated Ising (in absence of disorder), and
the higher being a Potts transition. Monte Carlo results clarify that in the
model with (or without) disorder the precursor phenomena are related to the
Griffiths (or Potts) transition. The Griffiths transition is a vanishing
transition which occurs above the Potts transition and is present only when
disorder is present, while the Potts transition which signals the effect due to
frustration is always present. These results suggest that precursor phenomena
in frustrated systems are due either to disorder and/or to frustration, giving
a consistent interpretation also for the limiting cases of Ising spin glass and
of Ising fully frustrated model, where also the Potts transition is vanishing.
This interpretation could play a relevant role in glassy systems beyond the
spin systems case.Comment: Completely rewritten. New data. New result
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
- …