328 research outputs found
First Order Phase Transition and Phase Coexistence in a Spin-Glass Model
We study the mean-field static solution of the Blume-Emery-Griffiths-Capel
model with quenched disorder, an Ising-spin lattice gas with quenched random
magnetic interaction. The thermodynamics is worked out in the Full Replica
Symmetry Breaking scheme. The model exhibits a high temperature/low density
paramagnetic phase. When the temperature is decreased or the density increased,
the system undergoes a phase transition to a Full Replica Symmetry Breaking
spin-glass phase. The nature of the transition can be either of the second
order
(like in the Sherrington-Kirkpatrick model) or, at temperature below a given
critical value (tricritical point), of the first order in the Ehrenfest sense,
with a discontinuous jump of the order parameter and a latent heat. In this
last case coexistence of phases occurs.Comment: 4 pages, 8 figure
Configurational entropy and the one-step RSB scenario in glasses
In this talk we discuss the possibility of constructing a fluctuation theory
for structural glasses in the non-equilibrium aging state. After reviewing well
known results in a toy model we discuss some of the key assumptions which
support the validity of this theory, in particular the role of the
configurational entropy and its relation to the effective temperature. Recent
numerical results for mean-field finite-size glasses agree with this scenario.Comment: Disordered and Complex Systems, 10-14 July 2000, Conference
Proceedings, 7 pages + 1 figur
Statistics of optimal information flow in ensembles of regulatory motifs
Genetic regulatory circuits universally cope with different sources of noise
that limit their ability to coordinate input and output signals. In many cases,
optimal regulatory performance can be thought to correspond to configurations
of variables and parameters that maximize the mutual information between inputs
and outputs. Such optima have been well characterized in several biologically
relevant cases over the past decade. Here we use methods of statistical field
theory to calculate the statistics of the maximal mutual information (the
`capacity') achievable by tuning the input variable only in an ensemble of
regulatory motifs, such that a single controller regulates N targets. Assuming
(i) sufficiently large N, (ii) quenched random kinetic parameters, and (iii)
small noise affecting the input-output channels, we can accurately reproduce
numerical simulations both for the mean capacity and for the whole
distribution. Our results provide insight into the inherent variability in
effectiveness occurring in regulatory systems with heterogeneous kinetic
parameters.Comment: 14 pages, 6 figure
Small clusters Renormalization Group in 2D and 3D Ising and BEG models with ferro, antiferro and quenched disordered magnetic interactions
The Ising and BEG models critical behavior is analyzed in 2D and 3D by means
of a renormalization group scheme on small clusters made of a few lattice
cells. Different kinds of cells are proposed for both ordered and disordered
model cases. In particular, cells preserving a possible antiferromagnetic
ordering under decimation allow for the determination of the N\'eel critical
point and its scaling indices. These also provide more reliable estimates of
the Curie fixed point than those obtained using cells preserving only the
ferromagnetic ordering. In all studied dimensions, the present procedure does
not yield the strong disorder critical point corresponding to the transition to
the spin-glass phase. This limitation is thoroughly analyzed and motivated.Comment: 14 pages, 12 figure
The Complex Spherical 2+4 Spin Glass: a Model for Nonlinear Optics in Random Media
A disordered mean field model for multimode laser in open and irregular
cavities is proposed and discussed within the replica analysis. The model
includes the dynamics of the mode intensity and accounts also for the possible
presence of a linear coupling between the modes, due, e.g., to the leakages
from an open cavity. The complete phase diagram, in terms of disorder strength,
source pumping and non-linearity, consists of four different optical regimes:
incoherent fluorescence, standard mode locking, random lasing and the novel
spontaneous phase locking. A replica symmetry breaking phase transition is
predicted at the random lasing threshold. For a high enough strength of
non-linearity, a whole region with nonvanishing complexity anticipates the
transition, and the light modes in the disordered medium display typical
discontinuous glassy behavior, i.e., the photonic glass has a multitude of
metastable states that corresponds to different mode-locking processes in
random lasers. The lasing regime is still present for very open cavities,
though the transition becomes continuous at the lasing threshold.Comment: 26 pages, 13 figure
Thermodynamic first order transition and inverse freezing in a 3D spin-glass
We present a numerical study of the random Blume-Capel model in three
dimension. The phase diagram is characterized by spin-glass/paramagnet phase
transitions both of first and second order in the thermodynamic sense.
Numerical simulations are performed using the Exchange-Monte Carlo algorithm,
providing clear evidence for inverse freezing. The main features at criticality
and in the phase coexistence region are investigated. We are not privy to other
3D short-range systems with quenched disorder undergoing inverse freezing.Comment: 4 pages, 3 figures
Stable Solution of the Simplest Spin Model for Inverse Freezing
We analyze the Blume-Emery-Griffiths model with disordered magnetic
interaction that displays the inverse freezing phenomenon. The behavior of this
spin-1 model in crystal field is studied throughout the phase diagram and the
transition and spinodal lines for the model are computed using the Full Replica
Symmetry Breaking Ansatz that always yields a thermodynamically stable phase.
We compare the results both with the formulation of the same model in terms of
Ising spins on lattice gas, where no reentrance takes place, and with the model
with generalized spin variables recently introduced by Schupper and Shnerb
[Phys. Rev. Lett. {\bf 93} 037202 (2004)], for which the reentrance is enhanced
as the ratio between the degeneracy of full to empty sites increases. The
simplest version of all these models, known as the Ghatak-Sherrington model,
turns out to hold all the general features characterizing an inverse transition
to an amorphous phase, including the right thermodynamic behavior.Comment: 4 pages, 4 figure
Statistical Field Theory and Effective Action Method for scalar Active Matter
We employ Statistical Field Theory techniques for coarse-graining the
steady-state properties of Active Ornstein-Uhlenbeck particles. The computation
is carried on in the framework of the Unified Colored Noise approximation that
allows an effective equilibrium picture. We thus develop a mean-field theory
that allows to describe in a unified framework the phenomenology of scalar
Active Matter. In particular, we are able to describe through spontaneous
symmetry breaking mechanism two peculiar features of Active Systems that are
(i) The accumulation of active particles at the boundaries of a confining
container, and (ii) Motility-Induced Phase Separation (MIPS).
\textcolor{black}{We develop a mean-field theory for steric interacting active
particles undergoing to MIPS and for Active Lennard-Jones (ALJ) fluids.}
\textcolor{black}{Within this framework}, we discuss the universality class of
MIPS and ALJ \textcolor{black}{showing that it falls into Ising universality
class.} We \textcolor{black}{thus} compute analytically the critical line
for both models. In the case of MIPS, gives rise to a
reentrant phase diagram compatible with an inverse transition from liquid to
gas as the strength of the noise decreases. \textcolor{black}{However, in the
case of particles interacting through anisotropic potentials, } the field
theory acquires a term that, \textcolor{black}{in general, cannot
be canceled performing the expansion around the critical point.} In this case,
the \textcolor{black}{Ising} critical point might \textcolor{black}{be
replaced} by a first-order phase transition \textcolor{black}{region}
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