Related papers: Deterministic Equations of Motion and Dynamic Crit…
Numerical methods for stochastic partial differential equations typically estimate moments of the solution from sampled paths. Instead, we shall directly target the deterministic equations satisfied by the first and second moments, as well…
With Monte Carlo simulations, we systematically investigate the depinning phase transition in the two-dimensional driven random-field clock model. Based on the short-time dynamic approach, we determine the transition field and critical…
We study various dynamical aspects of systems possessing a first order phase transition in their phase diagram. We isolate three qualitatively distinct types of theories depending on the structure of instabilities and the nature of the low…
A cyclic random motion at finite velocity with orthogonal directions is considered in the plane and in $\mathbb{R}^3$. We obtain in both cases the explicit conditional distributions of the position of the moving particle when the number of…
Finite-size effects in systems with diverging characteristic lengthscale have been addressed via state-of-the-art Monte Carlo and molecular dynamics simulations of various models exhibiting solid-solid, liquid-liquid and vapor-liquid…
A short-time dynamic approach to weak first order phase transitions is proposed. Taking the 2-dimensional Potts models as examples, from short-time behaviour of non-equilibrium relaxational processes starting from high temperature and zero…
A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state…
In this paper we study the short-time behavior of the Blume-Capel model at the tricritical point as well as along the second order critical line. Dynamic and static exponents are estimated by exploring scaling relations for 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…
We investigate spectral functions in the vicinity of the critical temperature of a second-order phase transition. Since critical phenomena in quantum field theories are governed by classical dynamics, universal properties can be computed…
We show that the short-time critical exponent $\theta$ related to the critical initial slip in a stochastic model can be determined by the time correlation of the order parameter. In our procedure it suffices to start with an uncorrelated…
Starting from the ordered state, we investigate the short-time behaviour of the hard-disk model. For the positional order, we determine the critical exponents eta and z from the dynamic relaxation of the order parameter and the cumulant…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…
The short-time dynamic evolution of an Ising model embedded in an infinitely ramified fractal structure with noninteger Hausdorff dimension was studied using Monte Carlo simulations. Completely ordered and disordered spin configurations…
We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees).…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. The three different bicritical static…
Dynamic discrete choice models often discretize the state vector and restrict its dimension in order to achieve valid inference. I propose a novel two-stage estimator for the set-identified structural parameter that incorporates a…
We report on classical Monte Carlo study of phase transitions and critical behavior of a 2D spin-pseudospin model describing a dilute magnet with competing charge and spin interactions. The static critical exponents of the specific heat and…
We present a calculation of critical phenomena directly in continuous dimension d employing an exact renormalization group equation for the effective average action. For an Ising-type scalar field theory we calculate the critical exponents…