115 research outputs found
Critical behaviour and ultrametricity of Ising spin-glass with long-range interactions
Ising spin-glass systems with long-range interactions () are considered. A numerical study of the critical behaviour is
presented in the non-mean-field region together with an analysis of the
probability distribution of the overlaps and of the ultrametric structure of
the space of the equilibrium configurations in the frozen phase. Also in
presence of diverging thermodynamical fluctuations at the critical point the
behaviour of the model is shown to be of the Replica Simmetry Breaking type and
there are hints of a non-trivial ultrametric structure. The parallel tempering
algorithm has been used to simulate the dynamical approach to equilibrium of
such systems.Comment: 15 pages and 12 figure
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
Complexity of waves in nonlinear disordered media
The statistical properties of the phases of several modes nonlinearly coupled
in a random system are investigated by means of a Hamiltonian model with
disordered couplings. The regime in which the modes have a stationary
distribution of their energies and the phases are coupled is studied for
arbitrary degrees of randomness and energy. The complexity versus temperature
and strength of nonlinearity is calculated. A phase diagram is derived in terms
of the stored energy and amount of disorder. Implications in random lasing,
nonlinear wave propagation and finite temperature Bose-Einstein condensation
are discussed.Comment: 20 pages, 11 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
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
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
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