228 research outputs found
Glass and polycrystal states in a lattice spin model
We numerically study a nondisordered lattice spin system with a first order
liquid-crystal transition, as a model for supercooled liquids and glasses.
Below the melting temperature the system can be kept in the metastable liquid
phase, and it displays a dynamic phenomenology analogous to fragile supercooled
liquids, with stretched exponential relaxation, power law increase of the
relaxation time and high fragility index. At an effective spinodal temperature
Tsp the relaxation time exceeds the crystal nucleation time, and the
supercooled liquid loses stability. Below Tsp liquid properties cannot be
extrapolated, in line with Kauzmann's scenario of a `lower metastability limit'
of supercooled liquids as a solution of Kauzmann's paradox. The off-equilibrium
dynamics below Tsp corresponds to fast nucleation of small, but stable, crystal
droplets, followed by extremely slow growth, due to the presence of pinning
energy barriers. In the early time region, which is longer the lower the
temperature, this crystal-growth phase is indistinguishable from an
off-equilibrium glass, both from a structural and a dynamical point of view:
crystal growth has not advanced enough to be structurally detectable, and a
violation of the fluctuation-dissipation theorem (FDT) typical of structural
glasses is observed. On the other hand, for longer times crystallization
reaches a threshold beyond which crystal domains are easily identified, and FDT
violation becomes compatible with ordinary domain growth.Comment: 25 page
On a universal mechanism for long ranged volatility correlations
We propose a general interpretation for long-range correlation effects in the
activity and volatility of financial markets. This interpretation is based on
the fact that the choice between `active' and `inactive' strategies is
subordinated to random-walk like processes. We numerically demonstrate our
scenario in the framework of simplified market models, such as the Minority
Game model with an inactive strategy. We show that real market data can be
surprisingly well accounted for by these simple models.Comment: Minor details changed, and Figure 4 improve
Population dynamics in a random environment
We investigate the competition between barrier slowing down and proliferation
induced superdiffusion in a model of population dynamics in a random force
field. Numerical results in suggest that a new intermediate diffusion
behaviour appears. We introduce the idea of proliferation assisted barrier
crossing and give a Flory like argument to understand qualitatively this non
trivial diffusive behaviour. A one loop RG analysis close to the critical
dimension d_c=2 confirms that the random force fixed point is unstable and
flows towards an uncontrolled strong coupling regime.Comment: 4 pages, 4 .eps figures. Submitted to Physical Review Letters
Corrected sign in flow equation, one figure changed, abstract changed.
Supersymmetric quenched complexity in the Sherrington-Kirkpatrick model
By using the BRST supersymmetry we compute the quenched complexity of the TAP
states in the SK model. We prove that the BRST complexity is equal to the
Legendre transform of the static free energy with respect to the largest
replica symmetry breaking point of its overlap matrix
Saddles on the potential energy landscape of a Lennard-Jones liquid
By means of molecular dynamics simulations, we study the stationary points of
the potential energy in a Lennard-Jones liquid, giving a purely geometric
characterization of the energy landscape of the system. We find a linear
relation between the degree of instability of the stationary points and their
potential energy, and we locate the energy where the instability vanishes. This
threshold energy marks the border between saddle-dominated and minima-dominated
regions of the energy landscape. The temperature where the potential energy of
the Stillinger-Weber minima becomes equal to the threshold energy turns out to
be very close to the mode-coupling transition temperature.Comment: Invited talk presented by A.C. at the Conference: Disordered and
Complex Systems, King's College London, July 200
Boundary information inflow enhances correlation in flocking
The most conspicuous trait of collective animal behaviour is the emergence of
highly ordered structures. Less obvious to the eye, but perhaps more profound a
signature of self-organization, is the presence of long-range spatial
correlations. Experimental data on starling flocks in 3d show that the exponent
ruling the decay of the velocity correlation function, C(r) ~ 1/r^\gamma, is
extremely small, \gamma << 1. This result can neither be explained by
equilibrium field theory, nor by off-equilibrium theories and simulations of
active systems. Here, by means of numerical simulations and theoretical
calculations, we show that a dynamical field applied to the boundary of a set
of Heisemberg spins on a 3d lattice, gives rise to a vanishing exponent \gamma,
as in starling flocks. The effect of the dynamical field is to create an
information inflow from border to bulk that triggers long range spin wave
modes, thus giving rise to an anomalously long-ranged correlation. The
biological origin of this phenomenon can be either exogenous - information
produced by environmental perturbations is transferred from boundary to bulk of
the flock - or endogenous - the flock keeps itself in a constant state of
dynamical excitation that is beneficial to correlation and collective response
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