Recently Dantas, Oliveira and Stilck [J. Stat. Mech. (2007) P08009] studied how the one-dimensional diffusive contact process crosses over from the critical behavior of directed percolation to an effective mean field behaviour when the diffusion rate is sent to infinity. They showed that this crossover can be described in terms of a crossover exponent $ϕ$, finding the boundaries 3 <= $ϕ$ <= 4 in one spatial dimension. In the present work we refine and extend this result up to four spatial dimensions by a field-theoretic calculation and extensive numerical simulations.
Phase Diagrams and Crossover in Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models
We consider the statistical properties of arrival times and balls on first-passage percolation (FPP) $2D$ square lattices with strong disorder in the link-times. A previous work showed a crossover in the weak disorder regime, between Gaussian and Kardar-Parisi-Zhang (KPZ) universality, with the crossover length decreasing as the noise amplitude grows. On the other hand, this work presents a very different behavior in the strong-disorder regime. A new crossover length appears below which the model is described by bond-percolation universality class. This characteristic length scale grows with t…
The dynamical properties of the invasion percolation on the square lattice are investigated with emphasis on the geometrical properties on the growing cluster of infected sites. The exterior frontier of this cluster forms a critical loop ensemble (CLE), whose length $(l)$, the radius $(r)$ and also roughness $(w)$ fulfill the finite size scaling hypothesis. The dynamical fractal dimension of the CLE defined as the exponent of the scaling relation between $l$ and $r$ is estimated to be $D_f=1.81\pm0.02$. By studying the autocorrelation functions of these quantities we show importantly that ther…
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different Lévy processes: in the first model we change gradually the order of the derivative in the Laplacian term of the diffusion equation, whereas in the second one we consider a combination of fractional-derivative diffusive terms characterized by coefficients that change in time. The proposals are illustrated by considering semi-analytical (i.e., analytical together with numerical) procedures to follo…
Novel ballistic to diffusive crossover in the dynamics of a one dimensional Ising model with variable range of interaction
自旋的动力学是由其相邻畴的大小决定的，这一观点是最近提出的（S。Biswas和P. Sen，Phys. Rev. E { \bf 80}，027101（2009））在伊辛自旋模型（此后，称为模型I）中进行。现在定义参数$p$以修改动力学，使得自旋可以在尺寸为$L$的一维系统中感测高达$R = pL/2$的畴尺寸。对于截止因子$p$ \to 0 $, the dynamics is Ising like and the domains grow with time $ t $ diffusively as $ t^{1/z} $ with $ z=2 $, while for $ p=1 $, the original model I showed ballistic dynamics with $ z \simeq 1 $. For intermediate values of $ p $, the domain growth, magnetisation and persistence show model I like behaviour up to a macroscopic crossover time $ t_1 \sim pL/2 $. Beyond $ t_1 $, characteristic power law variations of the dynamic …
Dynamical crossovers and correlations in a harmonic chain of active particles
International Center for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；Department of Physics and Astrophysics, University of Delhi（德里大学物理与天体物理学系）；Institute of Physics, Sachivalaya Marg（萨奇瓦亚亚玛格物理研究所）；Homi Bhabha National Institute（霍米·巴巴国民学院）
We study the history-dependent percolation in two dimensions, which evolves in generations from standard bond-percolation configurations through iteratively removing occupied bonds. Extensive simulations are performed for various generations on periodic square lattices up to side length $L=4096$. From finite-size scaling, we find that the model undergoes a continuous phase transition, which, for any finite number of generations, falls into the universality of standard 2D percolation. At the limit of infinite generation, we determine the correlation-length exponent $1/ν=0.828(5)$ and the fracta…
The critical behavior of the non-diffusive susceptible-infected-recovered model on lattices had been well established in virtue of its duality symmetry. By performing simulations and scaling analyses for the diffusive variant on the two-dimensional lattice, we show that diffusion for all agents, while rendering this symmetry destroyed, constitutes a singular perturbation that induces asymptotically distinct dynamical and stationary critical behavior from the non-diffusive model. In particular, the manifested crossover behavior in the effective mean-square radius exponents reveals that slow cro…
Unified theory for the scaling of the crossover between strong and weak disorder behaviors of optimal paths and directed/undirected polymers in disordered media
