2,724 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
Statistics of energy levels and zero temperature dynamics for deterministic spin models with glassy behaviour
We consider the zero-temperature dynamics for the infinite-range, non
translation invariant one-dimensional spin model introduced by Marinari, Parisi
and Ritort to generate glassy behaviour out of a deterministic interaction. It
is shown that there can be a large number of metatastable (i.e., one-flip
stable) states with very small overlap with the ground state but very close in
energy to it, and that their total number increases exponentially with the size
of the system.Comment: 25 pages, 8 figure
Energy Landscape Statistics of the Random Orthogonal Model
The Random Orthogonal Model (ROM) of Marinari-Parisi-Ritort [MPR1,MPR2] is a
model of statistical mechanics where the couplings among the spins are defined
by a matrix chosen randomly within the orthogonal ensemble. It reproduces the
most relevant properties of the Parisi solution of the Sherrington-Kirckpatrick
model. Here we compute the energy distribution, and work out an extimate for
the two-point correlation function. Moreover, we show exponential increase of
the number of metastable states also for non zero magnetic field.Comment: 23 pages, 6 figures, submitted to J. Phys.
Thermodynamical Limit for Correlated Gaussian Random Energy Models
Let \{E_{\s}(N)\}_{\s\in\Sigma_N} be a family of centered
unit Gaussian random variables defined by the covariance matrix of
elements \displaystyle c_N(\s,\tau):=\av{E_{\s}(N)E_{\tau}(N)}, and H_N(\s)
= - \sqrt{N} E_{\s}(N) the corresponding random Hamiltonian. Then the quenched
thermodynamical limit exists if, for every decomposition , and all
pairs (\s,\t)\in \Sigma_N\times \Sigma_N: c_N(\s,\tau)\leq \frac{N_1}{N}
c_{N_1}(\pi_1(\s),\pi_1(\tau))+ \frac{N_2}{N} c_{N_2}(\pi_2(\s),\pi_2(\tau))
where \pi_k(\s), k=1,2 are the projections of \s\in\Sigma_N into
. The condition is explicitly verified for the
Sherrington-Kirckpatrick, the even -spin, the Derrida REM and the
Derrida-Gardner GREM models.Comment: 15 pages, few remarks and two references added. To appear in Commun.
Math. Phy
A phase-separation perspective on dynamic heterogeneities in glass-forming liquids
We study dynamic heterogeneities in a model glass-former whose overlap with a
reference configuration is constrained to a fixed value. The system
phase-separates into regions of small and large overlap, so that dynamical
correlations remain strong even for asymptotic times. We calculate an
appropriate thermodynamic potential and find evidence of a Maxwell's
construction consistent with a spinodal decomposition of two phases. Our
results suggest that dynamic heterogeneities are the expression of an ephemeral
phase-separating regime ruled by a finite surface tension
Glassy dynamics, metastability limit and crystal growth in a lattice spin model
We introduce a lattice spin model where frustration is due to multibody
interactions rather than quenched disorder in the Hamiltonian. The system has a
crystalline ground state and below the melting temperature displays a dynamic
behaviour typical of fragile glasses. However, the supercooled phase loses
stability at an effective spinodal temperature, and thanks to this the Kauzmann
paradox is resolved. Below the spinodal the system enters an off-equilibrium
regime corresponding to fast crystal nucleation followed by slow activated
crystal growth. In this phase and in a time region which is longer the lower
the temperature we observe a violation of the fluctuation-dissipation theorem
analogous to structural glasses. Moreover, we show that in this system there is
no qualitative difference between a locally stable glassy configuration and a
highly disordered polycrystal
Silent Flocks
Experiments find coherent information transfer through biological groups on
length and time scales distinctly below those on which asymptotically correct
hydrodynamic theories apply. We present here a new continuum theory of
collective motion coupling the velocity and density fields of Toner and Tu to
the inertial spin field recently introduced to describe information propagation
in natural flocks of birds. The long-wavelength limit of the new equations
reproduces Toner-Tu theory, while at shorter wavelengths (or, equivalently,
smaller damping), spin fluctuations dominate over density fluctuations and
second sound propagation of the kind observed in real flocks emerges. We study
the dispersion relation of the new theory and find that when the speed of
second sound is large, a gap sharply separates first from second sound modes.
This gap implies the existence of `silent' flocks, namely medium-sized systems
across which neither first nor second sound can propagate
Quasifission and fusion-fission in massive nuclei reactions. Comparison of reactions leading to the Z=120 element
The yields of evaporation residues, fusion-fission and quasifission fragments
in the Ca+Sm and O+W reactions are analyzed
in the framework of the combined theoretical method based on the dinuclear
system concept and advanced statistical model. The measured yields of
evaporation residues for the Ca+Sm reaction can be well
reproduced. The measured yields of fission fragments are decomposed into
contributions coming from fusion-fission, quasifission, and fast-fission. The
decrease in the measured yield of quasifission fragments in
Ca+Sm at the large collision energies and the lack of
quasifission fragments in the Ca+Sm reaction are explained by
the overlap in mass-angle distributions of the quasifission and fusion-fission
fragments. The investigation of the optimal conditions for the synthesis of the
new element =120 (=302) show that the Cr+Cm reaction is
preferable in comparison with the Fe+Pu and Ni+U
reactions because the excitation function of the evaporation residues of the
former reaction is some orders of magnitude larger than that for the last two
reactions.Comment: 27 pages, 12 figures, submitted to Phys. Rev.
Off-equilibrium confined dynamics in a glassy system with level-crossing states
We study analytically the dynamics of a generalized p-spin model, starting
with a thermalized initial condition. The model presents birth and death of
states, hence the dynamics (even starting at equilibrium) may go out of
equilibrium when the temperature is varied. We give a full description of this
constrained out of equilibrium behavior and we clarify the connection to the
thermodynamics by computing (sub-dominant) TAP states, constrained to the
starting equilibrium configuration.Comment: 10 pages, 3 figures; longer version with appendi
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