We study the volatility of the S&P500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log-normal function. Further, using detrended fluctuation analysis we show that the volatility is power-law correlated with Hurst exponent α ≌ 0.9.

Employing detrended fluctuation analysis (DFA) and detrended cross-correlations analysis (DCCA), we analyze auto-correlations in the absolute returns for each of 30 Dow Jones Industrial Average (DJIA) constituents, Si, and cross-correlations in the absolute returns between the DJIA and each Si....

We describe a geometric approach for studying phase transitions, based upon the analysis of the “density of states” (DOS) functions (exact partition functions) for finite Ising systems. This approach presents a complementary method to the standard Monte Carlo method, since with a single...

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 study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path ℓopt in a disordered Erdős–Rényi (ER) random network and scale-free (SF) network. Each link i is associated with a weight τi≡exp(ari), where ri is a random number...