Related papers: Critical Dynamics of Self-Organizing Eulerian Walk…
Models of self-organized criticality, which can be described as singular diffusions with or without (multiplicative) Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models), are analyzed. Existence and uniqueness of…
The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed…
An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states,…
Dynamical phase transitions are nonequilibrium counterparts of thermodynamic phase transitions and share many similarities with their equilibrium analogs. In continuous phase transitions, critical exponents play a key role in characterizing…
A coupled phase-oscillator model consists of phase-oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is…
We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents omega>0. At the critical point the random and aperiodic systems…
We consider the diffusion scaling limit of the vicious walkers and derive the time-dependent spatial-distribution function of walkers. The dependence on initial configurations of walkers is generally described by using the symmetric…
The q-model is a random walk model used to describe the flow of stress in a stationary granular medium. Here we derive the exact horizontal and vertical correlation functions for the q-model in two dimensions. We show that close to a…
Effective field theories of two-dimensional lattice models of fluctuating loops are constructed by mapping them onto random surfaces whose large scale fluctuations are described by a Liouville field theory. This provides a geometrical view…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of…
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…
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…
We explore, employing the renormalization-group theory, the critical scaling behavior of the permutation symmetric three-vector model that obeys non-conserving dynamics and has a relevant anisotropic perturbation which drives the system…
Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and Kawasaki-type spin-exchange kinetics at infinite temperature T are investigated here in one dimension from the point of view of…
We study the critical dynamics of a scalar field theory with $Z_2$ symmetry in the dynamic universality class of Model A in two and three spatial dimensions with classical-statistical lattice simulations. In particular, we measure the…
The role of the distribution of coupling constants on the critical exponents of the short-range Ising spin-glass model is investigated via real space renormalization group. A saddle-point spin glass critical point characterized by a…
A globally driven self-organized critical model of earthquakes with conservative dynamics has been studied. An open but moving boundary condition has been used so that the origin (epicenter) of every avalanche (earthquake) is at the center…
The surface critical behaviour of the interacting self-avoiding trail is examined using transfer matrix methods coupled with finite-size scaling. Particular attention is paid to the critical exponents at the ordinary and special points…
Lattice models of coupled dynamical systems lead to a variety of complex behaviors. Between the individual motion of independent units and the collective behavior of members of a population evolving synchronously, there exist more…