Late stage, non-equilibrium dynamics in the dipolar Ising model

Magnetic domain structures are a fascinating area of study with interest deriving both from technological applications and fundamental scientific questions. The nature of the striped magnetic phases observed in ultra-thin films is one such intriguing system. The non-equilibrium dynamics of such systems as they evolve toward equilibrium has only recently become an area of interest and previous work on model systems showed evidence of complex, slow dynamics with glass-like properties as the stripes order mesoscopically. To aid in the characterization of the observed phases and the nature of the transitions observed in model systems we have developed an efficient method for identifying clusters or domains in the spin system, where the clusters are based on the stripe orientation. Thus we are able to track the growth and decay of such clusters of stripes in a Monte Carlo simulation and observe directly the nature of the slow dynamics. We have applied this method to consider the growth and decay of ordered domains after a quench from a saturated magnetic state to temperatures near and well below the critical temperature in the two dimensional dipolar Ising model. We discuss our method of identifying stripe domains or clusters of stripes within this model and present the results of our investigations.Comment: 17 pages, 12 figures, submitted to JMM

Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, we improve Conti's results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions.Comment: 29 pages, 3 figure

Universal finite-size scaling analysis of Ising models with long-range interactions at the upper critical dimensionality: Isotropic case

We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic whereby in the present work we focus on the isotropic case for which the model is found to be at its upper critical dimensionality. To investigate the critical behavior the temperature and field dependence of several quantities are studied by means of Monte Carlo simulations. On the basis of the Privman-Fisher hypothesis and results of the renormalization group the numerical data are analyzed in the framework of a finite-size scaling analysis and compared to finite-size scaling functions derived from a Ginzburg-Landau-Wilson model in zero mode (mean-field) approximation. The obtained excellent agreement suggests that at least in the present case the concept of universal finite-size scaling functions can be extended to the upper critical dimensionality.Comment: revtex4, 10 pages, 5 figures, 1 tabl

Phase diagram of an Ising model with long-range frustrating interactions: a theoretical analysis

We present a theoretical study of the phase diagram of a frustrated Ising model with nearest-neighbor ferromagnetic interactions and long-range (Coulombic) antiferromagnetic interactions. For nonzero frustration, long-range ferromagnetic order is forbidden, and the ground-state of the system consists of phases characterized by periodically modulated structures. At finite temperatures, the phase diagram is calculated within the mean-field approximation. Below the transition line that separates the disordered and the ordered phases, the frustration-temperature phase diagram displays an infinite number of ``flowers'', each flower being made by an infinite number of modulated phases generated by structure combination branching processes. The specificities introduced by the long-range nature of the frustrating interaction and the limitation of the mean-field approach are finally discussed.Comment: 32 pages, 7 figure

Calculation of The Critical Point for Two-Layer Ising and Potts Models Using Cellular Automata

The critical points of the two-layer Ising and Potts models for square lattice have been calculated with high precision using probabilistic cellular automata (PCA) with Glauber algorithm. The critical temperature is calculated for the isotropic and symmetric case (Kx=Ky=Kz=K), where Kx and Ky are the nearest-neighbor interactions within each layer in the x and y directions, respectively, and Kz is the interlayer coupling. The obtained results are 0.310 and 0.726 for two-layer Ising and Potts models, respectively, that are in good agreement with the accurate values reported by others

Progression of kidney disease in Indigenous Australians: the eGFR follow-up study

Background and objectives: Indigenous Australians experience a heavy burden of CKD. To address this burden, the eGFR Follow-Up Study recruited and followed an Indigenous Australian cohort from regions of Australia with the greatest ESRD burden. We sought to better understand factors contributing to the progression of kidney disease. Specific objectives were to assess rates of progression of eGFR in Indigenous Australians with and without CKD and identify factors associated with a decline in eGFR. Design, setting, participants, & measurements: This observational longitudinal study of Indigenous Australian adults was conducted in >20 sites. The baseline cohort was recruited from community and primary care clinic sites across five strata of health, diabetes status, and kidney function. Participants were then invited to follow up at 2–4 years; if unavailable, vital status, progression to RRT, and serum creatinine were obtained from medical records. Primary outcomes were annual eGFR change and combined renal outcome (first of ≥30% eGFR decline with follow-up eGFR<60 ml/min per 1.73 m2, progression to RRT, or renal death). Results: Participants (n=550) were followed for a median of 3.0 years. Baseline and follow-up eGFR (geometric mean [95% confidence interval], 83.9 (80.7 to 87.3) and 70.1 (65.9 to 74.5) ml/min per 1.73 m2, respectively. Overall mean annual eGFR change was −3.1 (−3.6 to −2.5) ml/min per 1.73 m2. Stratified by baseline eGFR (≥90, 60–89, 265 mg/g (30 mg/mmol). Baseline determinants of the combined renal outcome (experienced by 66 participants) were higher urine ACR, diabetes, lower measured GFR, and higher C-reactive protein. Conclusions: The observed eGFR decline was three times higher than described in nonindigenous populations. ACR was confirmed as a powerful predictor for eGFR decline across diverse geographic regions