Related papers: Critical dimensions of the diffusion equation
We investigate the evolution of the density-density correlations in the isoscalar critical condensate formed at the QCD critical point. The initial equilibrium state of the system is characterized by a fractal measure determining the…
We investigate the long-time evolution of branching diffusion processes (starting with a single particle) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. We analyze the…
The upper critical dimension of the Ising model is known to be $d_c=4$, above which critical behavior is regarded as trivial. We hereby argue from extensive simulations that, in the random-cluster representation, the Ising model…
The hysteresis loop in the zero-temperature random-field Ising model exhibits a critical point as the width of the disorder increases. Above six dimensions, the critical exponents of this transition, where the "infinite avalanche" first…
The homogeneous ordered state transforms into a polydomain state via a nucleation mechanism in two-dimensional lattice gas if the particle jumps are biased by an external field $E$. A simple phenomenological model is used to describe the…
By performing a high-statistics simulation of the $D=4$ random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high…
Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary…
The critical behavior of the random-field Ising model has been a puzzle for a long time. Different theoretical methods predict that the critical exponents of the random-field ferromagnet in D dimensions are the same as in the pure…
We study the diffusion front for a natural two-dimensional model where many particles starting at the origin diffuse independently. It turns out that this model can be described using properties of near-critical percolation, and provides a…
We determine the dimensional dependence of the percolative exponents of the jamming transition via numerical simulations in four and five spatial dimensions. These novel results complement literature ones, and establish jamming as a mixed…
Rugged (or, rough) energy landscape (REL) with spatially distributed maxima and minima are often employed in applications of physics, chemistry and biology (enzyme kinetics, protein folding, diffusion in disordered solids, transport in…
The critical behavior of semi-infinite systems in fixed dimensions $d<4$ is investigated theoretically. The appropriate extension of Parisi's massive field theory approach is presented.Two-loop calculations and subsequent Pad\'e-Borel…
We report measurements of the evolution of lines, planes, and volumes in an intensely turbulent laboratory flow using high-speed particle tracking. We find that the classical characteristic time scale of an eddy at the initial scale of the…
The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to…
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…
We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths ($D$). We found that $N>2$ cluster mean-field approximations must be considered to get consistent…
It is known that diffusion provokes substantial changes in continuous absorbing phase transitions. Conversely, its effect on discontinuous transitions is much less understood. In order to shed light in this direction, we study the inclusion…
Numerically we solve the microscopic deterministic equations of motion with random initial states for the two-dimensional $\phi^4$ theory. Scaling behavior of the persistence probability at criticality is systematically investigated and the…
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the…
The diffusion of particles trapped in long narrow channels occurs predominantly in one dimension. Here, molecular dynamics simulation is used to study the inertial dynamics of two-dimensional hard disks, confined to long, narrow,…