12 research outputs found
Phase diagram of an Ising model for ultrathin magnetic films
We study the critical properties of a two--dimensional Ising model with
competing ferromagnetic exchange and dipolar interactions, which models an
ultra-thin magnetic film with high out--of--plane anisotropy in the monolayer
limit. In this work we present a detailed calculation of the phase
diagram, being the ratio between exchange and dipolar interactions
intensities. We compare the results of both mean field approximation and Monte
Carlo numerical simulations in the region of low values of ,
identifying the presence of a recently detected phase with nematic order in
different parts of the phase diagram, besides the well known striped and
tetragonal liquid phases. A remarkable qualitative difference between both
calculations is the absence, in this region of the Monte Carlo phase diagram,
of the temperature dependency of the equilibrium stripe width predicted by the
mean field approximation. We also detected the presence of an increasing number
of metastable striped states as the value of increases.Comment: 9 pages, 9 figure
Homologous self-organising scale-invariant properties characterise long range species spread and cancer invasion
The invariance of some system properties over a range of temporal and/or spatial scales is an attribute of many processes in nature1, often characterised by power law functions and fractal geometry2. In particular, there is growing consensus in that fat-tailed functions like the power law adequately describe long-distance dispersal (LDD) spread of organisms 3,4. Here we show that the spatial spread of individuals governed by a power law dispersal function is represented by a clear and unique signature, characterised by two properties: A fractal geometry of the boundaries of patches generated by dispersal with a fractal dimension D displaying universal features, and a disrupted patch size distribution characterised by two different power laws. Analysing patterns obtained by simulations and real patterns from species dispersal and cell spread in cancer invasion we show that both pattern properties are a direct result of LDD and localised dispersal and recruitment, reflecting population self-organisation
Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models
The q-state Potts model with long-range interactions that decay as 1/r^alpha
subjected to an uniform magnetic field on d-dimensional lattices is analized
for different values of q in the nonextensive regime (alpha between 0 and d).
We also consider the two dimensional antiferromagnetic Ising model with the
same type of interactions. The mean field solution and Monte Carlo calculations
for the equations of state for these models are compared. We show that, using a
derived scaling which properly describes the nonextensive thermodynamic
behaviour, both types of calculations show an excellent agreement in all the
cases here considered, except for alpha=d. These results allow us to extend to
nonextensive magnetic models a previous conjecture which states that the mean
field theory is exact for the Ising one.Comment: 10 pages, 4 figure
Long-range interactions and non-extensivity in ferromagnetic spin models
The Ising model with ferromagnetic interactions that decay as is
analyzed in the non-extensive regime , where the
thermodynamic limit is not defined. In order to study the asymptotic properties
of the model in the limit ( being the number of spins)
we propose a generalization of the Curie-Weiss model, for which the
limit is well defined for all . We
conjecture that mean field theory is {\it exact} in the last model for all
. This conjecture is supported by Monte Carlo heat bath
simulations in the case. Moreover, we confirm a recently conjectured
scaling (Tsallis\cite{Tsallis}) which allows for a unification of extensive
() and non-extensive () regimes.Comment: RevTex, 12 pages, 1 eps figur
Scale-free correlations in the dynamics of a small (N ~ 10000) cortical network
The advent of novel opto-genetics technology allows the recording of brain
activity with a resolution never seen before. The characterisation of these
very large data sets offers new challenges as well as unique theory-testing
opportunities. Here we discuss whether the spatial and temporal correlation of
the collective activity of thousands of neurons are tangled as predicted by the
theory of critical phenomena. The analysis shows that both, the correlation
length and the correlation time scale as predicted as a function
of the system size. With some peculiarities that we discuss, the analysis
uncovers new evidence consistent with the view that the large scale brain
cortical dynamics corresponds to critical phenomena.Comment: 8 pages, 6 figure
Aging in a Two-Dimensional Ising Model with Dipolar Interactions
Aging in a two-dimensional Ising spin model with both ferromagnetic exchange
and antiferromagnetic dipolar interactions is established and investigated via
Monte Carlo simulations. The behaviour of the autocorrelation function
is analyzed for different values of the temperature, the waiting
time and the quotient , and being the
strength of exchange and dipolar interactions respectively. Different
behaviours are encountered for at low temperatures as is
varied. Our results show that, depending on the value of , the dynamics
of this non-disordered model is consistent either with a slow domain dynamics
characteristic of ferromagnets or with an activated scenario, like that
proposed for spin glasses.Comment: 4 pages, RevTex, 5 postscript figures; acknowledgment added and some
grammatical corrections in caption
Non-equilibrium Characterization of Spinodal Points using Short Time Dynamics
Though intuitively appealing, the concept of spinodal is rigourously defined
only in systems with infinite range interactions (mean field systems). In
short-range systems, a pseudo-spinodal can be defined by extrapolation of
metastable measurements, but the point itself is not reachable because it lies
beyond the metastability limit. In this work we show that a sensible definition
of spinodal points can be obtained through the short time dynamical behavior of
the system deep inside the metastable phase, by looking for a point where the
system shows critical behavior. We show that spinodal points obtained by this
method agree both with the thermodynamical spinodal point in mean field systems
and with the pseudo-spinodal point obtained by extrapolation of
meta-equilibrium behavior in short range systems. With this definition, a
practical determination can be achieved without regard for equilibration
issues.Comment: 10 pages, 12 figure
Call me by my name: unravelling the taxonomy of the gulper shark genus Centrophorus in the Mediterranean Sea through an integrated taxonomic approach
The current shift of fishery efforts towards the deep sea is raising concern about the vulnerability of deep-water sharks, which are often poorly studied and characterized by problematic taxonomy. For instance, in the Mediterranean Sea the taxonomy of genus Centrophorus has not been clearly unravelled yet. Since proper identification of the species is fundamental for their correct assessment and management, this study aims at clarifying the taxonomy of this genus in the Mediterranean Basin through an integrated taxonomic approach. We analysed a total of 281 gulper sharks (Centrophorus spp.) collected from various Mediterranean, Atlantic and Indian Ocean waters. Molecular data obtained from cytochrome c oxidase subunit I (COI), 16S ribosomal RNA (16S), NADH dehydrogenase subunit 2 (ND2) and a portion of a nuclear 28S ribosomal DNA gene region (28S) have highlighted the presence of a unique mitochondrial clade in the Mediterranean Sea. The morphometric results confirmed these findings, supporting the presence of a unique and distinct morphological group comprising all Mediterranean individuals. The data strongly indicate the occurrence of a single Centrophorus species in the Mediterranean, ascribable to C. cf. uyato, and suggest the need for a revision of the systematics of the genus in the area.En prens
Finite-size correlation behavior near a critical point: a simple metric for monitoring the state of a neural network
In this note, a correlation metric is proposed which is based on
the universal behavior of the linear/logarithmic growth of the correlation
length near/far the critical point of a continuous phase transition. The
problem is studied on a previously described neuronal network model for which
is known the scaling of the correlation length with the size of the observation
region. It is verified that the metric is maximized for the
conditions at which a power law distribution of neuronal avalanches sizes is
observed, thus characterizing well the critical state of the network. Potential
applications and limitations for its use with currently available optical
imaging techniques are discussed.Comment: 5 pages, 5 figure