Magnetic ordering in strong anisotropic ferromagnetic bilayers with dipolar and antiferromagnetic interlayer exchange interactions: Monte Carlo approach.

In this work, multilayer films consisting of two strong-anisotropic ferromagnetic layers antiferromagnetically coupled by a nonmagnetic spacer are studied by Monte Carlo simulations. The system is modeled by an Ising-based Hamiltonian that depends on both the intralayer exchange and dipolar constants and on the interlayer exchange constant (IEC). The ground state of the monolayers (null IEC) corresponds to alternate stripe domains with width h defined by the ratio between the exchange and dipolar constants (δ). The results show that IEC alters the energy balance that controls the stripe domain formation, leading to a ground state characterized by in-plane stripes out-plane antiferromagnetically coupled. When temperature increases two regimes are identified: an IEC-dominated regime where the orientational and positional orders are simultaneously lost in both layers, driving the system to the tetragonal liquid (TL) phase, and a dipolar-dominated one where signs of layers decoupling and the onset of positional disorder are observed. The last could be related with an intermediate nematic phase (NM). From the study of the nonequilibrium dynamics, the phase transitions to TL phase are characterized as continuous and those to the NM one as Kosterlitz-Thouless type. Also, for both layers the critical temperatures are the same and increase with IEC magnitude. Furthermore, the obtained critical exponents depend on the IEC values, which is indicative of a weak universality. For the dipolar-dominated regime, the decoupling between layers is also evidenced by the difference between their critical exponents.

Evidence of Kosterlitz-Thouless phase transitions in the Ising model with dipolar interactions.

The ferromagnetic bidimensional Ising model with dipolar interactions has been proposed to model ultrathin films with strong out-of-plane anisotropy. The phase diagram presents a rich phenomenology that includes low-temperature phases characterized by stripes of width n (h_{n}) and a high-temperature phase with domains of stripes with mutually perpendicular orientations, named tetragonal liquid (TL). The latter phase can be reached by two possible ways. One of them is the direct transition h_{n} to TL, and the other one is through an intermediate phase with orientational order but short-range positional disorder, named nematic phase (NM). The regions of the phase diagram where these transitions occur, as well as their character, remain an open question and are the object of the present work. In order to clarify this topic, intensive Monte Carlo simulations were performed by employing short-time dynamics as the main tool for studying the phase transition behavior. The dynamic evolution of the orientational order parameter and its moments are measured for selected values of the ratio between the ferromagnetic exchange and dipolar constants, called δ. The obtained results indicate that the intermediate NM phase is present for δ≥2 in narrow ranges of temperatures. Also, the results suggest that both transitions, i.e., h_{n}-NM and NM-TL, have a Kosterlitz-Thouless character. This type of topological transition is observed in continuous bidimensional models and have been proposed for discrete ones, as in the case of the present work.

Nanoclusters of crystallographically aligned nanoparticles for magnetic thermotherapy: aqueous ferrofluid, agarose phantoms and ex vivo melanoma tumour assessment.

Magnetic hyperthermia is an oncological therapy where magnetic nanostructures, under a radiofrequency field, act as heat transducers increasing tumour temperature and killing cancerous cells. Nanostructure heating efficiency depends both on the field conditions and on the nanostructure properties and mobility inside the tumour. Such nanostructures are often incorrectly bench-marketed in the colloidal state and using field settings far off from the recommended therapeutic values. Here, we prepared nanoclusters composed of iron oxide magnetite nanoparticles crystallographically aligned and their specific absorption rate (SAR) values were calorimetrically determined in physiological fluids, agarose-gel-phantoms and ex vivo tumours extracted from mice challenged with B16-F0 melanoma cells. A portable, multipurpose applicator using medical field settings; 100 kHz and 9.3 kA m-1, was developed and the results were fully analysed in terms of nanoclusters' structural and magnetic properties. A careful evaluation of the nanoclusters' heating capacity in the three milieus clearly indicates that the SAR values of fluid suspensions or agarose-gel-phantoms are not adequate to predict the real tissue temperature increase or the dosage needed to heat a tumour. Our results show that besides nanostructure mobility, perfusion and local thermoregulation, the nanostructure distribution inside the tumour plays a key role in effective heating. A suppression of the magnetic material effective heating efficiency appears in tumour tissue. In fact, dosage had to be increased considerably, from the SAR values predicted from fluid or agarose, to achieve the desired temperature increase. These results represent an important contribution towards the design of more efficient nanostructures and towards the clinical translation of hyperthermia.

Phase transitions and multicritical behavior in the Ising model with dipolar interactions.

In this work, the phase diagram of the ferromagnetic Ising model with dipole interactions is revisited with the aim of determining the nature of the phase transition between stripe-ordered phases with width n (h_{n}) and tetragonal liquid (TL) phases. Extensive Monte Carlo simulations are performed in order to study the short-time dynamic behavior of the observables for selected values of the ratio between the ferromagnetic exchange and dipolar constants δ. The obtained results indicate that the h_{1}-TL phase transition line is continuous up to δ=1.2585, while for the h_{2}-TL line a weak first-order character is found in the interval 1.2585≤δ≤1.36 and becomes continuous for 1.37≤δ≤1.9. This result suggests the existence of a tricritical point close to δ=1.37. When it is appropriate, the complete set of critical exponents is obtained, and in all the studied cases they depend on δ but do not belong to the Ising universality class. Furthermore, short-time dynamic studies reveal that at the point where the mentioned lines meet the h_{1}-h_{2} line, i.e., at δ=1.2585, the critical phase corresponding to the h_{1}-TL transition coexists with the h_{2} phase.

Phase transitions and critical phenomena in the two-dimensional Ising model with dipole interactions: A short-time dynamics study.

The ferromagnetic Ising model with antiferromagnetic dipole interactions is investigated by means of Monte Carlo simulations, focusing on the characterization of the phase transitions between the tetragonal liquid and stripe of width h phases. The dynamic evolution of the physical observables is analyzed within the short-time regime for 0.5≤δ≤1.3, where δ is the ratio between the short-range exchange and the long-range dipole interaction constants. The obtained results for the interval 0.5≤δ≤1.2 indicate that the phase transition line between the h=1 stripe and tetragonal liquid phases is continuous. This finding contributes to clarifying the controversy about the order of this transition. This controversy arises from the difficulties introduced in the simulations due to the presence of long-range dipole interactions, such as an important increase in the simulation times that limits the system size used, strong finite size effects, as well as to the existence of multiple metastable states at low temperatures. The study of the short-time dynamics of the model allows us to avoid these hindrances. Moreover, due to the fact that the finite-size effects do not significantly affect the power-law behavior exhibited in the observables within the short-time regime, the results could be attributed to those corresponding to the thermodynamic limit. As a consequence of this, a careful characterization of the critical behavior for the whole transition line is performed by giving the complete set of critical exponents.

Effective multidimensional crossover behavior in a one-dimensional voter model with long-range probabilistic interactions.

A variant of the standard voter model, where a randomly selected site of a one-dimensional lattice (d=1) adopts the state of another site placed at a distance r from the previous one, is proposed and studied by means of numerical simulations that are rationalized with the aid of dynamical and finite-size scaling arguments. The distance between the two sites is also selected randomly with a probability given by P(r)∝r(-(d+σ)), where σ is a control parameter. In this way one can study how the introduction of these long-range interactions influences the dynamic behavior of the standard voter model with nearest-neighbor interactions. It is found that the dynamics strongly depends on the range of the interactions, which is parameterized by σ, leading to an interesting effective multidimensional crossover behavior, as follows. (a) For σ<1 ordering is no longer observed and the average interface density [ρ(t)] assumes a steady state in the thermodynamic limit. Instead, for finite-size systems an exponential decay with a characteristic time (τ) that increases with the size is observed. This behavior resembles the scenario corresponding to the short-range voter model for d>2, as well as the case of both scale-free and small-world networks. (b) For σ>1, an ordering dynamics is observed, such that ρ(t)∝t(-α), where the exponent α increases with σ until it reaches the value α=1/2 for σ≥5, which corresponds to the behavior of the standard voter model with short-range interactions in d=1. (c) Finally, for σ≈1 we show evidence of a critical-type behavior as in the case of the critical dimension (d(c)=2) of the standard voter model.

Topological effects on the absorbing phase transition of the contact process in fractal media.

In a recent paper [S. B. Lee, Physica A 387, 1567 (2008)] the epidemic spread of the contact process (CP) in deterministic fractals, already studied by I. Jensen [J. Phys. A 24, L1111 (1991)], has been investigated by means of computer simulations. In these previous studies, epidemics are started from randomly selected sites of the fractal, and the obtained results are averaged all together. Motivated by these early works, here we also studied the epidemic behavior of the CP in the same fractals, namely, a Sierpinski carpet and the checkerboard fractals but averaging epidemics started from the same site. These fractal media have spatial discrete scale invariance symmetry, and consequently the dynamic evolution of some physical observables may become coupled to the topology, leading to the logarithmic-oscillatory modulation of the corresponding power laws. In fact, by means of extensive simulations we shown that the topology of the substrata causes the oscillatory behavior of the epidemic observables. However, in order to observe these oscillations, which have not been reported in earlier works, the interference effect arising during the averaging of epidemics started from nonequivalent sites should be eliminated. Finally, by analyzing our data and those available on the literature for the dependence of the exponents eta and delta on the dimensionality of substrata, we conjectured that for integer dimensions (2

Revisiting random walks in fractal media: on the occurrence of time discrete scale invariance.

This paper addresses the kinetic behavior of random walks in fractal media. We perform extensive numerical simulations of both single and annihilating random walkers on several Sierpinski carpets, in order to study the time behavior of three observables: the average number of distinct sites visited by a single walker, the mean-square displacement from the origin, and the density of annihilating random walkers. We found that the time behavior of those observables is given by a power law modulated by soft logarithmic-periodic oscillations. We conjecture that logarithmic-periodic oscillations are a manifestation of a time domain discrete scale iNvariance (DSI) that occurs as a consequence of the spatial DSI of the substrate. Our conjecture implies that the logarithmic periods of oscillations in space and time domains are linked by a dynamic exponent z, through z=log(tau)/log(b(1)), where tau and b(1) are the fundamental scaling ratios of the DSI symmetry in the time and space domains, respectively. We use this relationship in order to compute z for different observables and fractals. Furthermore, we check the values obtained with independent measurements provided by the power-law behavior of the mean-square displacement with time [R(2)(t) proportional variant t(2/z)]. The very good agreement obtained between both computations of the z exponent gives strong support to the idea of an intimate interplay between spatial and time symmetry properties that we expect will have a quite general scope. We expect that the application of the outlined concepts in the field of dynamic processes in fractal media will stimulate further research.

Discrete scale invariance effects in the nonequilibrium critical behavior of the Ising magnet on a fractal substrate.

The nonequilibrium critical dynamics of the Ising magnet on a fractal substrate, namely the Sierpinski carpet with Hausdorff dimension d(H)=1.7925, has been studied within the short-time regime by means of Monte Carlo simulations. The evolution of the physical observables was followed at criticality, after both annealing ordered spin configurations (ground state) and quenching disordered initial configurations (high temperature state), for three segmentation steps of the fractal. We have obtained evidence showing that during these relaxation processes both the growth and the fragmentation of magnetic domains become influenced by the hierarchical structure of the substrate. In fact, the interplay between the dynamic behavior of the magnet and the underlying fractal leads to the emergence of a logarithmic-periodic oscillation, superimposed to a power law, which has been observed in the time dependence of both the decay of the magnetization and its logarithmic derivative. These oscillations have been carefully characterized in order to determine the critical temperature of the second-order phase transition and the critical exponents corresponding to the short-time regime. The effects of the substrate can also be observed from the dependence of the effective critical exponents on the segmentation step. The exponent theta of the initial increase of the magnetization has also been obtained and the results suggest that it would be almost independent of the fractal dimension of the substrate, provided that d(H) is close enough to d=2. The oscillations have been discussed within the framework of the discrete scale invariance of the substrate.

Critical behavior of an Ising system on the Sierpinski carpet: a short-time dynamics study.

The short-time dynamic evolution of an Ising model embedded in an infinitely ramified fractal structure with noninteger Hausdorff dimension was studied using Monte Carlo simulations. Completely ordered and disordered spin configurations were used as initial states for the dynamic simulations. In both cases, the evolution of the physical observables follows a power-law behavior. Based on this fact, the complete set of critical exponents characteristic of a second-order phase transition was evaluated. Also, the dynamic exponent theta of the critical initial increase in magnetization, as well as the critical temperature, were computed. The exponent theta exhibits a weak dependence on the initial (small) magnetization. On the other hand, the dynamic exponent z shows a systematic decrease when the segmentation step is increased, i.e., when the system size becomes larger. Our results suggest that the effective noninteger dimension for the second-order phase transition is noticeably smaller than the Hausdorff dimension. Even when the behavior of the magnetization (in the case of the ordered initial state) and the autocorrelation (in the case of the disordered initial state) with time are very well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale.