We present a theoretical study of the effects of the next-nearest-neighbor (NNN) hopping (t2) on the properties of non-interacting bosons in optical lattices in the presence of an Aubry–André quasi-disorder. First we investigate, employing exact diagonalization, the effects of t2 on the...

In this paper, we study non-interacting bosons in a quasi-disordered one-dimensional optical lattice in a harmonic potential. We consider the case of deterministic quasi-disorder produced by an Aubry–André potential. Using exact diagonalization, we investigate both the zero temperature and...

We studied the ferromagnetic Ising model on two-dimensional systems with rough boundaries and several thickness distributions. First, we considered very long strips with discretized Gaussian distributions of widths with mean 3⩽L⩽12. Systems with fixed interface width W and with increasing...

The power series coherent anomaly method is applied to study the critical properties of a classical Heisenberg model. The values of true critical temperature Tc∗ are obtained. Using these results the estimation of critical exponent γ for the zero-field static susceptibility has been made. The...

According to many phenomenological and theoretical studies the distribution of family name frequencies in a population can be asymptotically described by a power law. We show that the Galton–Watson process corresponding to the dynamics of a growing population can be represented in Hilbert...

We study the spin-1 Blume–Capel model under a random crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal–Kadanoff technique. Interesting results are obtained, which tell us that the...

Starting from the well-known field theory for directed percolation (DP), we describe an evolving population, near extinction, in an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the environment follows a simple relaxational (Model A)...

The potential role of resummation techniques in the kinetic-theory approach to subgrid turbulence modeling is discussed.

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,...

The application of renormalization group (RG) theory to the asymptotic analysis of differential equations is considered. It is found that there is a class of small structural perturbations whose effects cannot be systematically treated using the Gell-Mann–Low RG approach applied in this...