Finite-size scaling of human-population distributions over fixed-size cells and its relation to fractal spatial structure.

Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases its variability when the size of the cells is increased. Nevertheless, the shape of the distributions is kept constant, which allows us to introduce a scaling law, analogous to finite-size scaling, with a scaling function reasonably well fitted by a gamma distribution. This means that the distribution of the number of inhabitants per cell is stable or invariant under addition with neighboring cells (plus rescaling), defying the central-limit theorem, due to the obvious dependence of the random variables. The finite-size scaling implies a power-law relations between the moments of the distribution and its scale parameter, which are found to be related with the fractal properties of the spatial pattern formed by the population. The match between theoretical predictions and empirical results is reasonably good.

Driving magnetic domains at the nanoscale by interfacial strain-induced proximity.

We investigate the local nanoscale changes of the magnetic anisotropy of a Ni film subject to an inverse magnetostrictive effect by proximity to a V2O3 layer. Using temperature-dependent photoemission electron microscopy (PEEM) combined with X-ray magnetic circular dichroism (XMCD), direct images of the Ni spin alignment across the first-order structural phase transition (SPT) of V2O3 were obtained. We find an abrupt temperature-driven reorientation of the Ni magnetic domains across the SPT, which is associated with a large increase of the coercive field. Moreover, angular dependent ferromagnetic resonance (FMR) shows a remarkable change in the magnetic anisotropy of the Ni film across the SPT of V2O3. Micromagnetic simulations based on these results are in quantitative agreement with the PEEM data. Direct measurements of the lateral correlation length of the Ni domains from XMCD images show an increase of almost one order of magnitude at the SPT compared to room temperature, as well as a broad spatial distribution of the local transition temperatures, thus corroborating the phase coexistence of Ni anisotropies caused by the V2O3 SPT. We show that the rearrangement of the Ni domains is due to strain induced by the oxide layers' structural domains across the SPT. Our results illustrate the use of alternative hybrid systems to manipulate magnetic domains at the nanoscale, which allows for engineering of coercive fields for novel data storage architectures.

From Boltzmann to Zipf through Shannon and Jaynes.

The word-frequency distribution provides the fundamental building blocks that generate discourse in natural language. It is well known, from empirical evidence, that the word-frequency distribution of almost any text is described by Zipf's law, at least approximately. Following Stephens and Bialek (2010), we interpret the frequency of any word as arising from the interaction potentials between its constituent letters. Indeed, Jaynes' maximum-entropy principle, with the constrains given by every empirical two-letter marginal distribution, leads to a Boltzmann distribution for word probabilities, with an energy-like function given by the sum of the all-to-all pairwise (two-letter) potentials. The so-called improved iterative-scaling algorithm allows us finding the potentials from the empirical two-letter marginals. We considerably extend Stephens and Bialek's results, applying this formalism to words with length of up to six letters from the English subset of the recently created Standardized Project Gutenberg Corpus. We find that the model is able to reproduce Zipf's law, but with some limitations: the general Zipf's power-law regime is obtained, but the probability of individual words shows considerable scattering. In this way, a pure statistical-physics framework is used to describe the probabilities of words. As a by-product, we find that both the empirical two-letter marginal distributions and the interaction-potential distributions follow well-defined statistical laws.