1,607 research outputs found

### A Hebbian approach to complex network generation

Through a redefinition of patterns in an Hopfield-like model, we introduce
and develop an approach to model discrete systems made up of many, interacting
components with inner degrees of freedom. Our approach clarifies the intrinsic
connection between the kind of interactions among components and the emergent
topology describing the system itself; also, it allows to effectively address
the statistical mechanics on the resulting networks. Indeed, a wide class of
analytically treatable, weighted random graphs with a tunable level of
correlation can be recovered and controlled. We especially focus on the case of
imitative couplings among components endowed with similar patterns (i.e.
attributes), which, as we show, naturally and without any a-priori assumption,
gives rise to small-world effects. We also solve the thermodynamics (at a
replica symmetric level) by extending the double stochastic stability
technique: free energy, self consistency relations and fluctuation analysis for
a picture of criticality are obtained

### Irreducible free energy expansion and overlaps locking in mean field spin glasses

We introduce a diagrammatic formulation for a cavity field expansion around
the critical temperature. This approach allows us to obtain a theory for the
overlap's fluctuations and, in particular, the linear part of the
Ghirlanda-Guerra relationships (GG) (often called Aizenman-Contucci polynomials
(AC)) in a very simple way. We show moreover how these constraints are
"superimposed" by the symmetry of the model with respect to the restriction
required by thermodynamic stability. Within this framework it is possible to
expand the free energy in terms of these irreducible overlaps fluctuations and
in a form that simply put in evidence how the complexity of the solution is
related to the complexity of the entropy.Comment: 19 page

### Ferromagnetic models for cooperative behavior: Revisiting Universality in complex phenomena

Ferromagnetic models are harmonic oscillators in statistical mechanics.
Beyond their original scope in tackling phase transition and symmetry breaking
in theoretical physics, they are nowadays experiencing a renewal applicative
interest as they capture the main features of disparate complex phenomena,
whose quantitative investigation in the past were forbidden due to data
lacking. After a streamlined introduction to these models, suitably embedded on
random graphs, aim of the present paper is to show their importance in a
plethora of widespread research fields, so to highlight the unifying framework
reached by using statistical mechanics as a tool for their investigation.
Specifically we will deal with examples stemmed from sociology, chemistry,
cybernetics (electronics) and biology (immunology).Comment: Contributing to the proceedings of the Conference "Mathematical
models and methods for Planet Heart", INdAM, Rome 201

### Diabolical points in the magnetic spectrum of Fe_8 molecules

The magnetic molecule Fe_8 has been predicted and observed to have a rich
pattern of degeneracies in its spectrum as an external magnetic field is
varied. These degeneracies have now been recognized to be diabolical points.
This paper analyzes the diabolicity and all essential properties of this system
using elementary perturbation theory. A variety of arguments is gievn to
suggest that an earlier semiclassical result for a subset of these points may
be exactly true for arbitrary spinComment: uses europhys.sty package; 3 embedded ps figure

### The replica symmetric behavior of the analogical neural network

In this paper we continue our investigation of the analogical neural network,
paying interest to its replica symmetric behavior in the absence of external
fields of any type. Bridging the neural network to a bipartite spin-glass, we
introduce and apply a new interpolation scheme to its free energy that
naturally extends the interpolation via cavity fields or stochastic
perturbations to these models. As a result we obtain the free energy of the
system as a sum rule, which, at least at the replica symmetric level, can be
solved exactly. As a next step we study its related self-consistent equations
for the order parameters and their rescaled fluctuations, found to diverge on
the same critical line of the standard Amit-Gutfreund-Sompolinsky theory.Comment: 17 page

### Equilibrium statistical mechanics on correlated random graphs

Biological and social networks have recently attracted enormous attention
between physicists. Among several, two main aspects may be stressed: A non
trivial topology of the graph describing the mutual interactions between agents
exists and/or, typically, such interactions are essentially (weighted)
imitative. Despite such aspects are widely accepted and empirically confirmed,
the schemes currently exploited in order to generate the expected topology are
based on a-priori assumptions and in most cases still implement constant
intensities for links. Here we propose a simple shift in the definition of
patterns in an Hopfield model to convert frustration into dilution: By varying
the bias of the pattern distribution, the network topology -which is generated
by the reciprocal affinities among agents - crosses various well known regimes
(fully connected, linearly diverging connectivity, extreme dilution scenario,
no network), coupled with small world properties, which, in this context, are
emergent and no longer imposed a-priori. The model is investigated at first
focusing on these topological properties of the emergent network, then its
thermodynamics is analytically solved (at a replica symmetric level) by
extending the double stochastic stability technique, and presented together
with its fluctuation theory for a picture of criticality. At least at
equilibrium, dilution simply decreases the strength of the coupling felt by the
spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main
difference with respect to previous investigations and a naive picture is that
within our approach replicas do not appear: instead of (multi)-overlaps as
order parameters, we introduce a class of magnetizations on all the possible
sub-graphs belonging to the main one investigated: As a consequence, for these
objects a closure for a self-consistent relation is achieved.Comment: 30 pages, 4 figure

### Analogue neural networks on correlated random graphs

We consider a generalization of the Hopfield model, where the entries of
patterns are Gaussian and diluted. We focus on the high-storage regime and we
investigate analytically the topological properties of the emergent network, as
well as the thermodynamic properties of the model. We find that, by properly
tuning the dilution in the pattern entries, the network can recover different
topological regimes characterized by peculiar scalings of the average
coordination number with respect to the system size. The structure is also
shown to exhibit a large degree of cliquishness, even when very sparse.
Moreover, we obtain explicitly the replica symmetric free energy and the
self-consistency equations for the overlaps (order parameters of the theory),
which turn out to be classical weighted sums of 'sub-overlaps' defined on all
possible sub-graphs. Finally, a study of criticality is performed through a
small-overlap expansion of the self-consistencies and through a whole
fluctuation theory developed for their rescaled correlations: Both approaches
show that the net effect of dilution in pattern entries is to rescale the
critical noise level at which ergodicity breaks down.Comment: 34 pages, 3 figure

### A linear Stark shift in dressed atoms as a signal to measure a nuclear anapole moment with a cold atom fountain or interferometer

We demonstrate theoretically the existence of a linear dc Stark shift of the
individual substates of an alkali atom in its ground state, dressed by a
circularly polarized laser field. It arises from the electroweak nuclear
anapole moment violating P but not T. It is characterized by the pseudoscalar
equal to the mixed product formed with the photon angular momentum and static
electric and magnetic fields. We derive the relevant left-right asymmetry with
its complete signature in a field configuration selected for a precision
measurement with cold atom beams. The 3,3 to 4,3 Cs hyperfine-transition
frequency shift amounts to 7 $\mu$Hz for a laser power of about 1 kW at 877 nm,
E=100 kV/cm and B larger than 0.5 G.Comment: Article, 4 pages, 2 figure

### Magnetization dynamics in the single-molecule magnet Fe8 under pulsed microwave irradiation

We present measurements on the single molecule magnet Fe8 in the presence of
pulsed microwave radiation at 118 GHz. The spin dynamics is studied via time
resolved magnetization experiments using a Hall probe magnetometer. We
investigate the relaxation behavior of magnetization after the microwave pulse.
The analysis of the experimental data is performed in terms of different
contributions to the magnetization after-pulse relaxation. We find that the
phonon bottleneck with a characteristic relaxation time of 10 to 100 ms
strongly affects the magnetization dynamics. In addition, the spatial effect of
spin diffusion is evidenced by using samples of different sizes and different
ways of the sample's irradiation with microwaves.Comment: 14 pages, 12 figure

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