Related papers: A Note on the Action in d>4 Dynamical Triangulatio…
Spin glass dynamics is a strong function of spatial dimensionality $D$. The lower critical dimension is close to 2.5, so that, in two dimensions, the condensation temperature $T_\text{g}=0$, and only fluctuations are present at finite…
The transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [5,9]. However, one may wonder if this…
Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…
In this paper we generalize the quantum mechanical model of three coupled oscillators because of its usage in the crystal optical activity. Using this model we can include the influence of all essential couplings between single oscillators…
For the O(N) sigma-model we studied the improvement program for actions with two- and four-spin interactions. An interesting example is an action which is reflection-positive, on-shell improved, and has all the coupling defined on an…
The critical behavior of the contact process in disordered and periodic binary 2d-lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory.…
We show that the phase transition previously observed in dynamical triangulation models of quantum gravity can be understood as being due to the creation of a singular link. The transition between singular and non-singular geometries as the…
We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip…
A driven Monte Carlo dynamics is introduced to study resistivity scaling in XY-type models in the phase representation. The method is used to study the phase transition of the three-dimensional XY spin glass with a Gaussian coupling…
I consider the problem of integrating a function $f$ over the $d$-dimensional unit cube. I describe a multilevel Monte Carlo method that estimates the integral with variance at most $\epsilon^{2}$ in $O(d+\ln(d)d_{t}\epsilon^{-2})$ time,…
We explore the two-dimensional generalized contact process with two absorbing states by means of large-scale Monte-Carlo simulations. In part of the phase diagram, an infinitesimal creation rate of active sites between inactive domains is…
The classical two-dimensional discrete frustrated $\phi ^4$ model is studied by Monte Carlo simulations. The correlation function is obtained for two values of a parameter $d$ that determines the frustration in the model. The ground state…
Finite-dimensional signatures of spinodal criticality are notoriously difficult to come by. The dynamical transition of glass-forming liquids, first described by mode-coupling theory, is a spinodal instability preempted by thermally…
We present the results of a study of the three-dimensional $XY$-model on a simple cubic lattice using the single cluster updating algorithm combined with improved estimators. We have measured the susceptibility and the correlation length…
In the framework of SOS models, the dynamics of isolated and pairs of surface steps of monoatomic height is studied, for step--edge diffusion and for evaporation kinetics, using Monte Carlo techniques. In particular, various interesting…
We perform Monte Carlo simulations of a gauge invariant spin system which describes random surfaces with gonihedric action in four dimensions. The Hamiltonian is a mixture of one-plaquette and additional two- and three-plaquette interaction…
Different dynamical symmetry breaking patterns are explored for the two dimensional phi4 model with higher order derivative terms. The one-loop saddle point expansion predicts a rather involved phase structure and a new Gaussian critical…
We describe a Monte Carlo procedure for the simulation of dynamically triangulate random surfaces with a boundary (topology of a disk). The algorithm keeps the total number of triangles fixed, while the length of the boundary is allowed to…
We explore the dynamical consequences of switching the coupling form in a system of coupled oscillators. We consider two types of switching, one where the coupling function changes periodically and one where it changes probabilistically. We…
We studied interplay between kinetic roughening and phase ordering in 1+1 dimensional single-step solid-on-solid growth model with two kinds of particles and Ising-like interaction. Evolution of both geometrical and compositional properties…