相关论文: Persistence in higher dimensions : a finite size s…
We study persistence in one-dimensional ferromagnetic and anti-ferromagnetic nearest-neighbor Ising models with parallel dynamics. The probability P(t) that a given spin has not flipped up to time t, when the system evolves from an initial…
Using a twisted nematic liquid crystal system exhibiting planar Ising model dynamics, we have measured the scaling exponent $\theta$ which characterizes the time evolution, $p(t) \sim t^{-\theta}$, of the probability p(t) that the local…
The distribution, n(k,t), of the interval sizes, k, between clusters of persistent sites in the dynamical evolution of the one-dimensional q-state Potts model is studied using a combination of numerical simulations, scaling arguments, and…
We define a block persistence probability $p_l(t)$ as the probability that the order parameter integrated on a block of linear size $l$ has never changed sign since the initial time in a phase ordering process at finite temperature T<T_c.…
The spatial distribution of persistent spins at zero-temperature in the pure two-dimensional Ising model is investigated numerically. A persistence correlation length, $\xi (t)\sim t^Z$ is identified such that for length scales $r<<\xi (t)$…
Persistence in coarsening 1D spin systems with a power law interaction $r^{-1-\sigma}$ is considered. Numerical studies indicate that for sufficiently large values of the interaction exponent $\sigma$ ($\sigma\geq 1/2$ in our simulations),…
The persistence exponents associated with the T=0 quenching dynamics of the two dimensional XY model and a two dimensional uniaxial spin nematic model have been evaluated using a numerical simulation. The site persistence or the probability…
We introduce a parameter $p$, called partial survival, in the persistence of stochastic processes and show that for smooth processes the persistence exponent $\theta(p)$ changes continuously with $p$, $\theta(0)$ being the usual persistence…
We have investigated the random walk problem in a finite system and studied the crossover induced in the the persistence probability scales by the system size.Analytical and numerical work show that the scaling function is an exponentially…
We investigate the life time distribution in one and two dimensional coarsening processes modelled by Ising - Glauber dynamics at zero temperature. We find that the life time distribution obeys a scaling ansatz, asymptotically. An…
We study the Persistence properties of the T=0 coarsening dynamics of one dimensional $q$-state Potts model using a modified mean-field approximation (MMFA). In this approximation, the spatial correlations between the interfaces separating…
The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is…
The dynamical evolution of the surface height is controlled by either a linear or a nonlinear Langevin equation, depending on the underlying microscopic dynamics, and is often done theoretically using stochastic coarse-grained growth…
The spatial distribution of persistent (unvisited) sites in one dimensional $A+A\to\emptyset$ model is studied. The `empty interval distribution' $n(k,t)$, which is the probability that two consecutive persistent sites are separated by…
The persistence exponent, theta, is defined by N_F sim t^theta, where t is the time since the start of the coarsening process and the "no-flip fraction", N_F, is the number of points that have not seen a change of "color" since t=0. Here we…
We consider the low-temperature coarsening dynamics of a one-dimensional Ising ferromagnet with conserved Kawasaki-like dynamics in the domain representation. Domains diffuse with size-dependent diffusion constant, $D(l) \propto l^\gamma$…
We consider the d-dimensional diffusion equation for a field phi(x,t) with random initial condition, and observe that, when appropriately scaled, phi(0,t) is Gaussian and Markovian in the limit d->0. This leads via the Majumdar-Sire…
{}From a finite-size scaling (FSS) theory of cumulants of the order parameter at phase coexistence points, we reconstruct the scaling of the moments. Assuming that the cumulants allow a reconstruction of the free energy density no better…
We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions $d=2$ and $3$. Results for the persistence probability and the domain growth…
Diffusion on a T fractal lattice under the influence of topological biasing fields is studied by finite size scaling methods. This allows to avoid proliferation and singularities which would arise in a renormalization group approach on…