Related papers: Long range to short range crossover in one dimensi…
The asymptotic behaviour of the survival or reunion probability of vicious walks with short-range interactions is generally well studied. In many realistic processes, however, walks interact with a long ranged potential that decays in $d$…
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
The finite-size critical properties of the ${\cal O}(n)$ vector $\phi^4$ model, with long-range interaction decaying algebraically with the interparticle distance $r$ like $r^{-d-\sigma}$, are investigated. The system is confined to a…
We present results of a Monte Carlo study for the ferromagnetic Ising model with long range interactions in two dimensions. This model has been simulated for a large range of interaction parameter $\sigma$ and for large sizes. We observe…
This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…
We consider the random transverse-field Ising model in $d=3$ dimensions with long-range ferromagnetic interactions which decay as a power $\alpha > d$ with the distance. Using a variant of the strong disorder renormalization group method we…
Relaxational processes in ordered phases of one-dimensional Ising models with long-range interactions are investigated by Monte Carlo simulations. Three types of spin model, the pure ferromagnetic, the diluted ferromagnetic, and the spin…
The study of critical properties of systems with long-range interactions has attracted in the last decades a continuing interest and motivated the development of several analytical and numerical techniques, in particular in connection with…
We have studied the one dimensional Dyson hierarchical model in presence of a random field. This is a long range model where the interactions scale with the distance with a power law-like form J(r) ~ r^{-\rho} and we can explore mean field…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
Interacting physical systems in the neighborhood of criticality (and massive continuum field theories) can often be characterized by just two physical scales: a (macroscopic) correlation length and a (microscopic) interaction range, related…
We consider a two-dimensional electron gas with long range disorder. Assuming that time reversal symmetry is broken either by an external magnetic field or, as in the case of a delta-correlated random magnetic field, by the disorder itself,…
We investigate the critical behavior of the one-dimensional Ising model with long-range interactions using the functional renormalization group in the local potential approximation (LPA), and compare our findings with Dyson's hierarchical…
We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power sigma of the distance. We show that there is a value of sigma of the long-range model for which…
We present an accurate numerical determination of the crossover from classical to Ising-like critical behavior upon approach of the critical point in three-dimensional systems. The possibility to vary the Ginzburg number in our simulations…
We model the one-dimension (1D) to three-dimension (3D) crossover in a cylindrically trapped Fermi gas with attractive interactions and spin-imbalance. We calculate the mean-field phase diagram, and study the relative stability of exotic…
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…
This article is aimed at studying the effects of the dimensional crossover (DC) on physical properties of condensed systems near phase transition and critical points. Here we consider the following problems: (1) the theoretical provisions…
Two-dimensional (2D) KPZ growth is usually investigated on substrates of lateral sizes $L_x=L_y$, so that $L_x$ and the correlation length ($\xi$) are the only relevant lengths determining the scaling behavior. However, in cylindrical…
We consider the phase-ordering kinetics of one-dimensional scalar systems. For attractive long-range ($r^{-(1+\sigma)}$) interactions with $\sigma>0$, ``Energy-Scaling'' arguments predict a growth-law of the average domain size $L \sim…