836 research outputs found
Elasticity and metastability limit in supercooled liquids: a lattice model
We present Monte Carlo simulations on a lattice system that displays a first
order phase transition between a disordered phase (liquid) and an ordered phase
(crystal). The model is augmented by an interaction that simulates the effect
of elasticity in continuum models. The temperature range of stability of the
liquid phase is strongly increased in the presence of the elastic interaction.
We discuss the consequences of this result for the existence of a kinetic
spinodal in real systems.Comment: 8 pages, 5 figure
Role of saddles in mean-field dynamics above the glass transition
Recent numerical developments in the study of glassy systems have shown that
it is possible to give a purely geometric interpretation of the dynamic glass
transition by considering the properties of unstable saddle points of the
energy. Here we further develop this program in the context of a mean-field
model, by analytically studying the properties of the closest saddle point to
an equilibrium configuration of the system. We prove that when the glass
transition is approached the energy of the closest saddle goes to the threshold
energy, defined as the energy level below which the degree of instability of
the typical stationary points vanishes. Moreover, we show that the distance
between a typical equilibrium configuration and the closest saddle is always
very small and that, surprisingly, it is almost independent of the temperature
Coarsening Dynamics of a Nonconserved Field Advected by a Uniform Shear Flow
We consider the ordering kinetics of a nonconserved scalar field advected by
a uniform shear flow. Using the Ohta-Jasnow-Kawasaki approximation, modified to
allow for shear-induced anisotropy, we calculate the asymptotic time dependence
of the characteristic length scales, L_parallel and L_perp, that describe the
growth of order parallel and perpendicular to the mean domain orientation. In
space dimension d=3 we find, up to constants, L_parallel = gamma t^{3/2},
L_perp = t^{1/2}, where gamma is the shear rate, while for d = 2 we find
L_parallel = gamma^{1/2} t (ln t)^{1/4}, L_perp = gamma^{-1/2}(ln t)^{-1/4} .
Our predictions for d=2 can be tested by experiments on twisted nematic liquid
crystals.Comment: RevTex, 4 page
On the stationary points of the TAP free energy
In the context of the p-spin spherical model, we introduce a method for the
computation of the number of stationary points of any nature (minima, saddles,
etc.) of the TAP free energy. In doing this we clarify the ambiguities related
to the approximations usually adopted in the standard calculations of the
number of states in mean field spin glass models.Comment: 11 pages, 1 Postscript figure, plain Te
Basins of attraction of metastable states of the spherical -spin model
We study the basins of attraction of metastable states in the spherical
-spin spin glass model, starting the relaxation dynamics at a given distance
from a thermalized condition. Weighting the initial condition with the
Boltzmann distribution we find a finite size for the basins. On the contrary, a
white weighting of the initial condition implies vanishing basins of
attraction. We make the corresponding of our results with the ones of a
recently constructed effective potential.Comment: LaTeX, 7 pages, 7 eps figure
Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses
The structure of states of the perturbed p-spin spherical spin-glass is
analyzed. At low enough free energy metastable states have a supersymmetric
structure, while at higher free energies the supersymmetry is broken. The
transition between the supersymmetric and the supersymmetry-breaking phase is
triggered by a change in the stability of states
Geometric approach to the dynamic glass transition
We numerically study the potential energy landscape of a fragile glassy
system and find that the dynamic crossover corresponding to the glass
transition is actually the effect of an underlying geometric transition caused
by a qualitative change in the topological properties of the landscape.
Furthermore, we show that the potential energy barriers connecting local glassy
minima increase with decreasing energy of the minima, and we relate this
behaviour to the fragility of the system. Finally, we analyze the real space
structure of activated processes by studying the distribution of particle
displacements for local minima connected by simple saddles
Dynamical quenching and annealing in self-organization multiagent models
We study the dynamics of a generalized Minority Game (GMG) and of the Bar
Attendance Model (BAM) in which a number of agents self-organize to match an
attendance that is fixed externally as a control parameter. We compare the
usual dynamics used for the Minority Game with one for the BAM that makes a
better use of the available information. We study the asymptotic states reached
in both frameworks. We show that states that can be assimilated to either
thermodynamic equilibrium or quenched configurations can appear in both models,
but with different settings. We discuss the relevance of the parameter that
measures the value of the prize for winning in units of the fine for losing. We
also provide an annealing protocol by which the quenched configurations of the
GMG can progressively be modified to reach an asymptotic equlibrium state that
coincides with the one obtained with the BAM.Comment: around 20 pages, 10 figure
Statistical mechanics of the mixed majority-minority game with random external information
We study the asymptotic macroscopic properties of the mixed majority-minority
game, modeling a population in which two types of heterogeneous adaptive
agents, namely ``fundamentalists'' driven by differentiation and
``trend-followers'' driven by imitation, interact. The presence of a fraction f
of trend-followers is shown to induce (a) a significant loss of informational
efficiency with respect to a pure minority game (in particular, an efficient,
unpredictable phase exists only for f<1/2), and (b) a catastrophic increase of
global fluctuations for f>1/2. We solve the model by means of an approximate
static (replica) theory and by a direct dynamical (generating functional)
technique. The two approaches coincide and match numerical results
convincingly.Comment: 19 pages, 3 figure
Spin-Glass Theory for Pedestrians
In these notes the main theoretical concepts and techniques in the field of
mean-field spin-glasses are reviewed in a compact and pedagogical way, for the
benefit of the graduate and undergraduate student. One particular spin-glass
model is analyzed (the p-spin spherical model) by using three different
approaches. Thermodynamics, covering pure states, overlaps, overlap
distribution, replica symmetry breaking, and the static transition. Dynamics,
covering the generating functional method, generalized Langevin equation,
equations for the correlation and the response, the Mode Coupling
approximation, and the dynamical transition. And finally complexity, covering
the mean-field (TAP) free energy, metastable states, entropy crisis, threshold
energy, and saddles. Particular attention has been paid on the mutual
consistency of the results obtained from the different methods.Comment: Lecture notes of the school: "Unifying Concepts in Glassy Physics
III", Bangalore, June 200
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