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 $(\delta,T)$ phase diagram, $\delta$ 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 $\delta$, 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 $\delta$ increases.Comment: 9 pages, 9 figure

Thermodynamics from a scaling Hamiltonian

There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both extensive and nonextensive thermodynamic perspectives. We use a model, whose Hamiltonian takes into account spins ferromagnetically coupled in a chain via a power law that decays at large interparticle distance $r$ as $1/r^{\alpha}$ for $\alpha\geq0$. Here, we review old nonextensive scaling. In addition, we propose a new Hamiltonian scaled by $2\frac{(N/2)^{1-\alpha}-1}{1-\alpha}$ that explicitly includes symmetry of the lattice and dependence on the size, $N$, of the system. The new approach enabled us to improve upon previous results. A numerical test is conducted through Monte Carlo simulations. In the model, periodic boundary conditions are adopted to eliminate surface effects.Comment: 12 pages, 2 figures, submitted for publication to Phys. Rev.

Pattern formation in the dipolar Ising model on a two-dimensional honeycomb lattice

We present Monte Carlo simulation results for a two-dimensional Ising model with ferromagnetic nearest-neighbor couplings and a competing long-range dipolar interaction on a honeycomb lattice. Both structural and thermodynamic properties are very similar to the case of a square lattice, with the exception that structures reflect the sixfold rotational symmetry of the underlying honeycomb lattice. To deal with the long-range nature of the dipolar interaction we also present a simple method of evaluating effective interaction coefficients, which can be regarded as a more straightforward alternative to the prevalent Ewald summation techniques.Comment: 5 pages, 5 figure

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.Comment: 910 pages, 10 figure

The exchange bias phenomenon in uncompensated interfaces: Theory and Monte Carlo simulations

We performed Monte Carlo simulations in a bilayer system composed by two thin films, one ferromagnetic (FM) and the other antiferromagnetic (AFM). Two lattice structures for the films were considered: simple cubic (sc) and a body center cubic (bcc). In both lattices structures we imposed an uncompensated interfacial spin structure, in particular we emulated a FeF2-FM system in the case of the (bcc) lattice. Our analysis focused on the incidence of the interfacial strength interactions between the films J_eb and the effect of thermal fluctuations on the bias field H_EB. We first performed Monte Carlo simulations on a microscopic model based on classical Heisenberg spin variables. To analyze the simulation results we also introduced a simplified model that assumes coherent rotation of spins located on the same layer parallel to the interface. We found that, depending on the AFM film anisotropy to exchange ratio, the bias field is either controlled by the intrinsic pinning of a domain wall parallel to the interface or by the stability of the first AFM layer (quasi domain wall) near the interface.Comment: 18 pages, 11 figure

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

Clifford-Finsler Algebroids and Nonholonomic Einstein-Dirac Structures

We propose a new framework for constructing geometric and physical models on nonholonomic manifolds provided both with Clifford -- Lie algebroid symmetry and nonlinear connection structure. Explicit parametrizations of generic off-diagonal metrics and linear and nonlinear connections define different types of Finsler, Lagrange and/or Riemann-Cartan spaces. A generalization to spinor fields and Dirac operators on nonholonomic manifolds motivates the theory of Clifford algebroids defined as Clifford bundles, in general, enabled with nonintegrable distributions defining the nonlinear connection. In this work, we elaborate the algebroid spinor differential geometry and formulate the (scalar, Proca, graviton, spinor and gauge) field equations on Lie algebroids. The paper communicates new developments in geometrical formulation of physical theories and this approach is grounded on a number of previous examples when exact solutions with generic off-diagonal metrics and generalized symmetries in modern gravity define nonholonomic spacetime manifolds with uncompactified extra dimensions.Comment: The manuscript was substantially modified following recommendations of JMP referee. The former Chapter 2 and Appendix were elliminated. The Introduction and Conclusion sections were modifie

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