209 research outputs found
Dynamical arrest, tracer diffusion and Kinetically Constrained Lattice Gases
We analyze the tagged particle diffusion for kinetically constrained models
for glassy systems. We present a method, focusing on the Kob-Andersen model as
an example, which allows to prove lower and upper bounds for the self diffusion
coefficient . This method leads to the exact density dependence of
, at high density, for models with finite defects and to prove
diffusivity, , at any finite density for highly cooperative models. A
more general outcome is that under very general assumptions one can exclude
that a dynamical transition, like the one predicted by the Mode-Coupling-Theory
of glasses, takes place at a finite temperature/chemical potential for systems
of interacting particles on a lattice.Comment: 28 pages, 4 figure
Random Pinning Glass Transition: Hallmarks, Mean-Field Theory and Renormalization Group Analysis
We present a detailed analysis of glass transitions induced by pinning
particles at random from an equilibrium configuration. We first develop a
mean-field analysis based on the study of p-spin spherical disordered models
and then obtain the three dimensional critical behavior by the Migdal-Kadanoff
real space renormalization group method. We unveil the important physical
differences with the case in which particles are pinned from a random (or very
high temperature) configuration. We contrast the pinning particles approach to
the ones based on biasing dynamical trajectories with respect to their activity
and on coupling to equilibrium configurations. Finally, we discuss numerical
and experimental tests.Comment: Submitted for publication in J. Chem. Phys. for the special topic
issue on the glass transition. 28 Page
Spiral Model: a cellular automaton with a discontinuous glass transition
We introduce a new class of two-dimensional cellular automata with a
bootstrap percolation-like dynamics. Each site can be either empty or occupied
by a single particle and the dynamics follows a deterministic updating rule at
discrete times which allows only emptying sites. We prove that the threshold
density for convergence to a completely empty configuration is non
trivial, , contrary to standard bootstrap percolation. Furthermore
we prove that in the subcritical regime, , emptying always occurs
exponentially fast and that coincides with the critical density for
two-dimensional oriented site percolation on \bZ^2. This is known to occur
also for some cellular automata with oriented rules for which the transition is
continuous in the value of the asymptotic density and the crossover length
determining finite size effects diverges as a power law when the critical
density is approached from below. Instead for our model we prove that the
transition is {\it discontinuous} and at the same time the crossover length
diverges {\it faster than any power law}. The proofs of the discontinuity and
the lower bound on the crossover length use a conjecture on the critical
behaviour for oriented percolation. The latter is supported by several
numerical simulations and by analytical (though non rigorous) works through
renormalization techniques. Finally, we will discuss why, due to the peculiar
{\it mixed critical/first order character} of this transition, the model is
particularly relevant to study glassy and jamming transitions. Indeed, we will
show that it leads to a dynamical glass transition for a Kinetically
Constrained Spin Model. Most of the results that we present are the rigorous
proofs of physical arguments developed in a joint work with D.S.Fisher.Comment: 42 pages, 11 figure
Fluctuations and shape of cooperative rearranging regions in glass-forming liquids
We develop a theory of amorphous interfaces in glass-forming liquids. We show that the statistical properties of these surfaces, which separate regions characterized by different amorphous arrangements of particles, coincide with the ones of domain walls in the random field Ising model. A major consequence of our results is that supercooled liquids are characterized by two different static lengths: the point-to-set ΟPS, which is a measure of the spatial extent of cooperative rearranging regions, and the wandering length Οâ„, which is related to the fluctuations of their shape. We find that Ο℠grows when approaching the glass transition but slower than ΟPS. The wandering length increases as sâ1/2c, where sc is the configurational entropy. Our results strengthen the relationship with the random field Ising model found in recent works. They are in agreement with previous numerical studies of amorphous interfaces and provide a theoretical framework for explaining numerical and experimental findings on pinned particle systems and static lengths in glass-forming liquids
Breakdown of Elasticity in Amorphous Solids
What characterises a solid is its way to respond to external stresses.
Ordered solids, such crystals, display an elastic regime followed by a plastic
one, both well understood microscopically in terms of lattice distortion and
dislocations. For amorphous solids the situation is instead less clear, and the
microscopic understanding of the response to deformation and stress is a very
active research topic. Several studies have revealed that even in the elastic
regime the response is very jerky at low temperature, resembling very much the
one of disordered magnetic materials. Here we show that in a very large class
of amorphous solids this behaviour emerges by decreasing the temperature as a
phase transition where standard elastic behaviour breaks down. At the
transition all non-linear elastic modulii diverge and standard elasticity
theory does not hold anymore. Below the transition the response to deformation
becomes history and time-dependent.Comment: 3 figure
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