While the Ising model on the Cayley tree has no spontaneous magnetization at nonzero temperatures in the thermodynamic limit, we show that finite systems of astronomical sizes remain magnetically ordered in a wide temperature range, if the symmetry is broken by fixing an arbitrary single (bulk...

In this work we present the first exact solution of a system of interacting particles with phase transitions of order higher than two. The presented analytical derivation shows that the Ising model on the Cayley tree exhibits a line of third order phase transition points, between temperatures...

We present a novel approach to pattern recognition, based on mapping of images onto a multidimensional parameter space defined by a long range interaction Ising model Hamiltonian. It is shown that different character patterns occupy mutually distant points within the n-dimensional space defined...

We examine statistical properties of a daily hot pixel time series recorded in Brazil during the period 1998–2006, using Multifractal Detrended Fluctuation Analysis (MF-DFA). We find that generalized scaling exponent h(q) is a decreasing function of q, indicating multifractal behavior of hot...

Owing to extremely slow decay of correlations, the limit H → 0 presents a poor approximation for the Ising model on the Sierpiński gasket. We present evidence of the competitive interplay between finite size scaling and thermodynamic scaling for this model, where both finite size and finite...

We investigate multifractal properties of daily price changes in currency rates using the multifractal detrended fluctuation analysis (MF-DFA). We analyze managed and independent floating currency rates in eight countries, and determine the changes in multifractal spectrum when transitioning...

We study auto-correlations and cross-correlations of daily price changes and daily volume changes of thirteen global stock market indices, using multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DXA). We find rather distinct...

We analyze correlations and cross-correlations in wind speed and solar radiation temporal series recorded at the Island Fernando de Noronha in northeastern Brazil, using Detrended fluctuation analysis (DFA) and Detrended cross-correlation analysis (DCCA). We find that both processes exhibit...

We investigate the auto-correlations and cross-correlations of the volatility time series in the Brazilian stock and commodity market, using the recently introduced Detrended Cross-Correlation Analysis. We find that the auto-correlations in stock volatilities are weaker than the...

In this work, we apply Detrended Fluctuation Analysis (DFA) to study the dynamics of electrical cortical activity in rats during the phenomenon of Cortical Spreading Depression (CSD), as well as the periods before and after this phenomenon. The characteristic of CSD is reduced electrical...