This paper examines the long memory property in the conditional variance of the G7’s major stock market indices, using the FIGARCH model. The GARCH and IGARCH frameworks are also estimated for comparative purposes.

The Bak–Sneppen model of co-evolution is used to derive synthetic time series with a priori specified fractal dimension (or Hurst exponent) through a mixing of processes in various lattice dimensions. Both theoretical and numerical analyses concern the avalanches at the critical threshold and...

In this paper, using both analytic methods and Monte Carlo simulations with our triangle cluster algorithm, we illustrate the scaling behavior of two possible 4th-order connected energy cumulants across the well-known second and first-order phase transitions of the Baxter–Wu model under zero...

The double perovskite (DP) Sr2CrReO6, with its high Curie temperature, is a good candidate for magneto-electric and magneto-optic applications. Thus, a theoretical study by Monte Carlo Simulation (MCS) and Mean Field Approximation (MFA) in the context of the Ising model is important for a better...

Using mean-field renormalization group (MFRG) and surface-bulk mean-field renormalization group (SBMFRG) methods, we study the critical properties of classical Heisenberg and XY models. We show the exact result that there is no finite temperature phase transition in one dimension and very good...

We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the Swendsen–Wang and Wolff cluster algorithms....

The four-dimensional Ising model is simulated on the Creutz cellular automaton. The computed values of the critical temperature, the static critical exponents for the order parameter, the magnetic susceptibility, the specific heat, and the linear dynamical critical exponent for the order...

A method is developed to calculate the critical line of two dimensional (2D) anisotropic Ising model including nearest-neighbor interactions. The method is based on the real-space renormalization group (RG) theory with increasing block sizes. The reduced temperatures, Ks (where K=JkBT and J, kB,...

We have studied a model of self-interacting branched polymers on the three-dimensional Sierpinski gasket lattice, in the presence of an attractive impenetrable fractal boundary. Using an exact renoramlization group approach, we have determined the phase diagram boundaries of this model, and its...