arXiv subjects

S. A. Cannas

Publications and source records attributed to S. A. Cannas.

13 recordsLinked to original sources

arXiv2016

Critical exponents and scaling invariance in the absence of a critical point

The paramagnetic-to-ferromagnetic phase transition is believed to proceed through a critical point, at which power laws and scaling invariance, associated with the existence of one diverging characteristic length scale -- the so called correlation length -- appear. We indeed observe power laws and scaling behavior over extraordinarily many decades of the suitable scaling variables at the paramagnetic-to-ferromagnetic phase transition in ultrathin Fe films. However, we find that, when the putative critical point is approached, the singular behavior of thermodynamic quantities transforms into an analytic one: the critical point does not exist, it is replaced by a more complex phase involving domains of opposite magnetization, below as well as $above$ the putative critical temperature. All essential experimental results are reproduced by Monte-Carlo simulations in which, alongside the familiar exchange coupling, the competing dipole-dipole interaction is taken into account. Our results imply that a scaling behavior of macroscopic thermodynamic quantities is not necessarily a signature for an underlying second-order phase transition and that the paramagnetic-to-ferromagnetic phase transition proceeds, very likely, in the presence of at least two long spatial scales: the correlation length and the size of magnetic domains.

cond-mat.stat-mech↗

arXiv2014

Anisotropy-based mechanism for zigzag striped patterns in magnetic thin films

In this work we studied a two dimensional ferromagnetic system using Monte Carlo simulations. Our model includes exchange and dipolar interactions, a cubic anisotropy term, and uniaxial out-of-plane and in-plane ones. According to the set of parameters chosen, the model including uniaxial out-of-plane anisotropy has a ground-state which consists of a canted state with stripes of opposite out-of-plane magnetization. When the cubic anisotropy is introduced zigzag patterns appear in the stripes at fields close to the remanence. An analysis of the anisotropy terms of the model shows that this configuration is related to specific values of the ratio between the cubic and the effective uniaxial anisotropy. The mechanism behind this effect is related to particular features of the anisotropy's energy landscape, since a global minima transition as a function of the applied field is required in the anisotropy terms. This new mechanism for zigzags formation could be present in monocrystal ferromagnetic thin films in a given range of thicknesses.

cond-mat.mtrl-sci↗

arXiv2013

Critical behavior of self-assembled rigid rods on two-dimensional lattices: Bethe-Peierls approximation and Monte Carlo simulations

The critical behavior of adsorbed monomers that reversibly polymerize into linear chains with restricted orientations relative to the substrate has been studied. In the model considered here, which is known as self-assembled rigid rods (SAARs) model, the surface is represented by a twodimensional lattice and a continuous orientational transition occurs as a function of temperature and coverage. The phase diagrams were obtained for the square, triangular and honeycomb lattices by means of Monte Carlo simulations and finite-size scaling analysis. The numerical results were compared with Bethe-Peierls analytical predictions about the orientational transition for the square and triangular lattices. The analysis of the phase diagrams, along with the behavior of the critical average rod lengths, showed that the critical properties of the model do not depend on the structure of the lattice at low temperatures (coverage), revealing a one-dimensional behavior in this regime. Finally, the universality class of the SAARs model, which has been subject of controversy, has been revisited.

cond-mat.stat-mech↗

arXiv2010

Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results.

cond-mat.stat-mech↗

arXiv2009

Emergent self-organized complex network topology out of stability constraints

Although most networks in nature exhibit complex topology the origins of such complexity remains unclear. We introduce a model of a growing network of interacting agents in which each new agent's membership to the network is determined by the agent's effect on the network's global stability. It is shown that out of this stability constraint, scale free networks emerges in a self organized manner, offering an explanation for the ubiquity of complex topological properties observed in biological networks.

cond-mat.dis-nn↗

arXiv2009

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 $(δ,T)$ phase diagram, $δ$ 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 $δ$, 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 $δ$ increases.

cond-mat.stat-mech↗

arXiv2008

Interplay between coarsening and nucleation in an Ising model with dipolar interactions

We study the dynamical behavior of a square lattice Ising model with exchange and dipolar interactions by means of Monte Carlo simulations. After a sudden quench to low temperatures we find that the system may undergo a coarsening process where stripe phases with different orientations compete or alternatively it can relax initially to a metastable nematic phase and then decay to the equilibrium stripe phase through nucleation. We measure the distribution of equilibration times for both processes and compute their relative probability of occurrence as a function of temperature and system size. This peculiar relaxation mechanism is due to the strong metastability of the nematic phase, which goes deep in the low temperature stripe phase. We also measure quasi-equilibrium autocorrelations in a wide range of temperatures. They show a distinct decay to a plateau that we identify as due to a finite fraction of frozen spins in the nematic phase. We find indications that the plateau is a finite size effect. Relaxation times as a function of temperature in the metastable region show super-Arrhenius behavior, suggesting a possible glassy behavior of the system at low temperatures.

cond-mat.stat-mech↗

arXiv2007

Similar self-organizing scale-invariant properties characterize early cancer invasion and long range species spread

Occupancy of new habitats through dispersion is a central process in nature. In particular, long range dispersal is involved in the spread of species and epidemics, although it has not been previously related with cancer invasion, a process that involves spread to new tissues. We show that the early spread of cancer cells is similar to the species individuals spread and that both processes are represented by a common spatio-temporal signature, characterized by a particular fractal geometry of the boundaries of patches generated, and a power law-scaled, disrupted patch size distribution. We show that both properties are a direct result of long-distance dispersal, and that they reflect homologous ecological processes of population self-organization. Our results are significant for processes involving long-range dispersal like biological invasions, epidemics and cancer metastasis.

q-bio.PE↗

arXiv2006

Ising nematic phase in ultra-thin magnetic films: a Monte Carlo study

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. We present numerical evidence showing that two different scenarios appear in the model for different values of the exchange to dipolar intensities ratio, namely, a single first order stripe - tetragonal phase transition or two phase transitions at different temperatures with an intermediate Ising nematic phase between the stripe and the tetragonal ones. Our results are very similar to those predicted by Abanov et al [Phys. Rev. B 51, 1023 (1995)], but suggest a much more complex critical behavior than the predicted by those authors for both the stripe-nematic and the nematic-tetragonal phase transitions. We also show that the presence of diverging free energy barriers at the stripe-nematic transition makes possible to obtain by slow cooling a metastable supercooled nematic state down to temperatures well below the transition one.

cond-mat.stat-mech↗

arXiv2003

Slow dynamics in a 2D Ising model with competing interactions

The far-from-equilibrium low-temperature dynamics of ultra-thin magnetic films is analyzed by using Monte Carlo numerical simulations on a two dimensional Ising model with competing exchange ($J_0$) and dipolar ($J_d$) interactions. In particular, we focus our attention on the low temperature region of the $(δ,T)$ phase diagram (where $δ= J_0/J_d$) for the range of values of $δ$ where striped phases with widths $h=1$ ($h1$) and $h=2$ ($h2$) are present. The presence of metastable states of the phase $h2$ in the region where the phase $h1$ is the thermodynamically stable one and viceversa was established recently. In this work we show that the presence of these metastable states appears as a blocking mechanism that slows the dynamics of magnetic domains growth when the system is quenched from a high temperature state to a low temperature state in the region of metastability.

cond-mat.dis-nn↗

arXiv2000

Out of Equilibrium Dynamics of the Hopfield Model in its spin-glass phase

In this work we study numerically the out of equilibrium dynamics of the Hopfield model for associative memory inside its spin-glass phase. Besides its interest as a neural network model it can also be considered as a prototype of fully connected magnetic systems with randomness and frustration. By adjusting the ratio between the number of stored configurations $p$ and the total number of neurons $N$ one can control the phase-space structure, whose complexity can vary between the simple mean-field ferromagnet (when $p=1$) and that of the Sherrington-Kirkpatrick spin-glass model (for a properly taken limit of an infinite number of patterns). In particular, little attention has been devoted to the spin-glass phase of this model. In this work we analyse the two-time auto-correlation function, the decay of the magnetization and the distribution of overlaps between states. The results show that within the spin-glass phase of the model the dynamics exhibits ageing phenomena and presents features that suggest a non trivial breaking of replica symmetry.

cond-mat.dis-nn↗

arXiv1999

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.

cond-mat.dis-nn↗

arXiv1996

Long-range interactions and non-extensivity in ferromagnetic spin models

The Ising model with ferromagnetic interactions that decay as $1/r^α$ is analyzed in the non-extensive regime $0\leqα\leq d$, where the thermodynamic limit is not defined. In order to study the asymptotic properties of the model in the $N\rightarrow\infty$ limit ($N$ being the number of spins) we propose a generalization of the Curie-Weiss model, for which the $N\rightarrow\infty$ limit is well defined for all $α\geq 0$. We conjecture that mean field theory is {\it exact} in the last model for all $0\leqα\leq d$. This conjecture is supported by Monte Carlo heat bath simulations in the $d=1$ case. Moreover, we confirm a recently conjectured scaling (Tsallis\cite{Tsallis}) which allows for a unification of extensive ($α>d$) and non-extensive ($0\leqα\leq d$) regimes.

cond-mat↗