We use the Migdal–Kadanoff renormalization group technique to study the spin-3/2 Blume–Capel model under a random crystal field, in the two- and three-dimensional cases. Studying the fixed points and the phase diagrams established, we find interesting results allowing us to understand the...

Using a real-space renormalization group procedure with no adjustable parameters, we investigate the Blume-Emery-Griffiths model on the square lattice. The formalism respects sublattice symmetry, allowing the study of both signs of K, the biquadratic exchange coupling. Our results for K 0 are...

Using field-theoretical methods and exploiting conformal invariance, we study Casimir forces at tricritical points exerted by long-range fluctuations of the order-parameter field. Special attention is paid to the situation where the symmetry is broken by the boundary conditions (extraordinary...

We calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non-overlapping generations. Each ancestor at generation g in the past has a weight w which is (up to a normalization) the...

The purpose of this work is the investigation of critical dynamic properties of two strongly coupled paramagnetic sublattices exhibiting a paramagnetic–ferrimagnetic transition. To go beyond the mean-field approximation, and in order to get a correct critical dynamic behavior, use is made of...

The purpose of this paper is the application of a usual method of statistical mechanics—the renormalization based on Wilson's recursive relations—in order to study the critical behavior of a social index, namely the live births per 1000 population. The drastic decreases of this index on...

We apply a physical-based model to describe the clothes fashion market. Every time a new outlet appears on the market, it can invade the market under certain specific conditions. Hence, the “old” outlet can be completely dominated and disappears. Each creator competes for a finite population...

In this paper, a mode of using the Dynamic Renormalization Group (DRG) method is suggested in order to cope with inconsistent results obtained when applying it to a continuous family of one-dimensional nonlocal models. The key observation is that the correct fixed-point dynamical system has to...

The field theory renormalization group is used for analyzing the fractional Langevin equation with the order of the temporal derivative 0α1, fractional Laplacian of the order σ, and Gaussian noise correlator. The case of non-linearity φm with odd m≥3 is considered. It is proved that the...

We revisit quantum criticality of d-dimensional n-vector transverse Ising-like models by means of a conventional one-loop renormalization group (RG) approach with temperature scaling. Focusing on dimensionalities d≤3, a careful analysis of the quantum regime allows us to explore the...