187 research outputs found
Microscopic energy flows in disordered Ising spin systems
An efficient microcanonical dynamics has been recently introduced for Ising
spin models embedded in a generic connected graph even in the presence of
disorder i.e. with the spin couplings chosen from a random distribution. Such a
dynamics allows a coherent definition of local temperatures also when open
boundaries are coupled to thermostats, imposing an energy flow. Within this
framework, here we introduce a consistent definition for local energy currents
and we study their dependence on the disorder. In the linear response regime,
when the global gradient between thermostats is small, we also define local
conductivities following a Fourier dicretized picture. Then, we work out a
linearized "mean-field approximation", where local conductivities are supposed
to depend on local couplings and temperatures only. We compare the approximated
currents with the exact results of the nonlinear system, showing the
reliability range of the mean-field approach, which proves very good at high
temperatures and not so efficient in the critical region. In the numerical
studies we focus on the disordered cylinder but our results could be extended
to an arbitrary, disordered spin model on a generic discrete structures.Comment: 12 pages, 6 figure
Instability and network effects in innovative markets
We consider a network of interacting agents and we model the process of
choice on the adoption of a given innovative product by means of
statistical-mechanics tools. The modelization allows us to focus on the effects
of direct interactions among agents in establishing the success or failure of
the product itself. Mimicking real systems, the whole population is divided
into two sub-communities called, respectively, Innovators and Followers, where
the former are assumed to display more influence power. We study in detail and
via numerical simulations on a random graph two different scenarios:
no-feedback interaction, where innovators are cohesive and not sensitively
affected by the remaining population, and feedback interaction, where the
influence of followers on innovators is non negligible. The outcomes are
markedly different: in the former case, which corresponds to the creation of a
niche in the market, Innovators are able to drive and polarize the whole
market. In the latter case the behavior of the market cannot be definitely
predicted and become unstable. In both cases we highlight the emergence of
collective phenomena and we show how the final outcome, in terms of the number
of buyers, is affected by the concentration of innovators and by the
interaction strengths among agents.Comment: 20 pages, 6 figures. 7th workshop on "Dynamic Models in Economics and
Finance" - MDEF2012 (COST Action IS1104), Urbino (2012
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
A Two-populations Ising model on diluted Random Graphs
We consider the Ising model for two interacting groups of spins embedded in
an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are
investigated by means of extensive Monte Carlo simulations. Our results
evidence the existence of a phase transition at a value of the inter-groups
interaction coupling which depends algebraically on the dilution of
the graph and on the relative width of the two populations, as explained by
means of scaling arguments. We also measure the critical exponents, which are
consistent with those of the Curie-Weiss model, hence suggesting a wide
robustness of the universality class.Comment: 11 pages, 4 figure
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
Fractal geometry of Ising magnetic patterns: signatures of criticality and diffusive dynamics
We investigate the geometric properties displayed by the magnetic patterns
developing on a two-dimensional Ising system, when a diffusive thermal dynamics
is adopted. Such a dynamics is generated by a random walker which diffuses
throughout the sites of the lattice, updating the relevant spins. Since the
walker is biased towards borders between clusters, the border-sites are more
likely to be updated with respect to a non-diffusive dynamics and therefore, we
expect the spin configurations to be affected. In particular, by means of the
box-counting technique, we measure the fractal dimension of magnetic patterns
emerging on the lattice, as the temperature is varied. Interestingly, our
results provide a geometric signature of the phase transition and they also
highlight some non-trivial, quantitative differences between the behaviors
pertaining to the diffusive and non-diffusive dynamics
Universal features of information spreading efficiency on -dimensional lattices
A model for information spreading in a population of mobile agents is
extended to -dimensional regular lattices. This model, already studied on
two-dimensional lattices, also takes into account the degeneration of
information as it passes from one agent to the other. Here, we find that the
structure of the underlying lattice strongly affects the time at which
the whole population has been reached by information. By comparing numerical
simulations with mean-field calculations, we show that dimension is
marginal for this problem and mean-field calculations become exact for .
Nevertheless, the striking nonmonotonic behavior exhibited by the final degree
of information with respect to and the lattice size appears to be
geometry independent.Comment: 8 pages, 9 figure
Autocatalytic reaction-diffusion processes in restricted geometries
We study the dynamics of a system made up of particles of two different
species undergoing irreversible quadratic autocatalytic reactions: . We especially focus on the reaction velocity and on the average time at
which the system achieves its inert state. By means of both analytical and
numerical methods, we are also able to highlight the role of topology in the
temporal evolution of the system
Autocatalytic reaction-diffusion processes in restricted geometries
We study the dynamics of a system made up of particles of two different
species undergoing irreversible quadratic autocatalytic reactions: . We especially focus on the reaction velocity and on the average time at
which the system achieves its inert state. By means of both analytical and
numerical methods, we are also able to highlight the role of topology in the
temporal evolution of the system
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