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Various physical models can be expressed in terms of matrices. A valuable tool for analysing matrix models is numerical simulations, often the Metropolis algorithm with various improvements. The downside of this approach is that the…
We report numerical investigations of a three-dimensional model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in, and exchanges…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
The dynamics of complex systems generally include high-dimensional, non-stationary and non-linear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties we detail a new approach based…
We study the Metropolis dynamics of a simple spin system without disorder, which exhibits glassy dynamics at low temperatures. We use an implementation of the algorithm of Bortz, Kalos and Lebowitz \cite{bortz}. This method turns out to be…
Recent results concerning the topological properties of random geometrical sets have been successfully applied to the study of the morphology of clusters in percolation theory. This approach provides an alternative way of inspecting the…
We review the local Monte Carlo dynamics and Swendsen-Wang cluster algorithm. We introduce and analyze a new Monte Carlo dynamics known as transitional Monte Carlo. The transitional Monte Carlo algorithm samples energy probability…
For $d \ge 2$ and all $q\geq q_{0}(d)$ we give an efficient algorithm to approximately sample from the $q$-state ferromagnetic Potts and random cluster models on finite tori $(\mathbb Z / n \mathbb Z )^d$ for any inverse temperature…
We classify four-state spin models with interactions along the edges according to their behavior under a specific group of symmetry transformations. This analysis uses the measure of complexity of the action of the symmetries, in the spirit…
In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy.…
We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well…
A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +- J spin-glass models. Using the genetic cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are…
In this article, we investigate symmetry properties of distributed systems of mobile robots. We consider a swarm of $n\in\mathbb{N}$ robots in the $\mathcal{OBLOT}$ model and analyze their collective $\mathcal{F}$sync dynamics using of…
The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface order parameters and susceptibilities and…
Through Monte Carlo simulations we study two-dimensional Potts models with $q=4, 6$ and 8 states on Voronoi-Delaunay random lattice. In this study, we assume that the coupling factor $J$ varies with the distance $r$ between the first…
Using Monte Carlo simulations in the frame of stochastic series expansion (SSE), we study the three-state quantum Potts model. The cluster algorithm we used is a direct generalization of that for the quantum Ising model. The simulations…
We use Monte Carlo simulations to study the static and dynamical properties of a Potts glass with infinite range Gaussian distributed exchange interactions for a broad range of temperature and system size up to N=2560 spins. The results are…
Using mappings to computer-science problems and by applying sophisticated algorithms, one can study numerically many problems much better compared to applying standard approaches like Monte Carlo simulations. Here, using calculations of…
A spin dynamics algorithm, combining checkerboard updating and a rotation algorithm based on the local second-rank ordering field, is developed for the Lebwohl-Lasher model of liquid crystals. The method is shown to conserve energy well and…
We present an adaptive algorithm which optimizes the statistical-mechanical ensemble in a generalized broad-histogram Monte Carlo simulation to maximize the system's rate of round trips in total energy. The scaling of the mean round-trip…