Related papers: Numerical simulation study of the dynamical behavi…
We show that addition of Metropolis single spin-flips to the Wolff cluster flipping Monte Carlo procedure leads to a dramatic {\bf increase} in performance for the spin-1/2 Ising model. We also show that adding Wolff cluster flipping to the…
We formulate a single-cluster Monte Carlo algorithm for the simulation of the random-cluster model. This algorithm is a generalization of the Wolff single-cluster method for the $q$-state Potts model to non-integer values $q>1$. Its results…
We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we…
We simulated the fourier transform of the correlation function of the Ising model in two and three dimensions using a single cluster algorithm with improved estimators. The simulations are in agreement with series expansion and the…
Many spin systems affected by critical slowing down can be efficiently simulated using cluster algorithms. Where such systems have long-range interactions, suitable formulations can additionally bring down the computational effort for each…
Simulations of the two-dimensional Ising and 3-state Potts models at their critical points are performed using the invaded cluster (IC) algorithm. It is argued that observables measured on a sub-lattice of size l should exhibit a crossover…
We explore the dynamics of artificial one- and two-dimensional Ising-like quantum antiferromagnets with different lattice geometries by using a Rydberg quantum simulator of up to 36 spins in which we dynamically tune the parameters of the…
We perform numerical simulations to study static and dynamic critical behaviour of the 3d random-site Ising model. A distinct feature of our approach is a combination of the Metropolis, Swendsen-Wang, and Wolff Monte Carlo algorithms. For…
Despite several attempts, no efficient cluster algorithm has been constructed for CP(N-1) models in the standard Wilson formulation of lattice field theory. In fact, there is a no-go theorem that prevents the construction of an efficient…
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform…
We describe a method to study the rate at which modes decorrelate in numerical simulations. We study the XY model updated with the Metropolis and Wolff dynamics respectively and compute the rate at which each eigenvector of the dynamics…
Spin systems with frustration and disorder are notoriously difficult to study both analytically and numerically. While the simulation of ferromagnetic statistical mechanical models benefits greatly from cluster algorithms, these accelerated…
We propose an algorithm that builds and maintains clusters over a network subject to mobility. This algorithm is fully decentralized and makes all the different clusters grow concurrently. The algorithm uses circulating tokens that collect…
We investigate the approach to stable and metastable equilibrium in Ising models using a cluster representation. The distribution of nucleation times is determined using the Metropolis algorithm and the corresponding $\phi^{4}$ model using…
The dynamic critical behavior of the two-replica cluster algorithm is studied. Several versions of the algorithm are applied to the two-dimensional, square lattice Ising model with a staggered field. The dynamic exponent for the full…
We propose a pair of completely data-driven algorithms for unsupervised classification and dimension reduction, and we empirically study their performance on a number of data sets, both simulated data in three-dimensions and images from the…
Using the Metropolis algorithm, we simulate the relaxation process of the three-dimensional kinetic Ising model. Starting from a random initial configuration, we first present the average equilibration time across the entire phase boundary.…
We present a self consistent method based on cluster algorithms and Renormalization Group on the lattice to study critical systems numerically. We illustrate it by means of the 2D Ising model. We compute the critical exponents $\nu$ and…
On directed Barabasi-Albert networks with two and seven neighbours selected by each added site, the Ising model does not seem to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation follows an…
We have studied the magnetic relaxation behavior of a two-dimensional Ising ferromagnet by Monte Carlo simulation. Our primary goal is to investigate the effects of the system's geometry (area preserving) , boundary conditions, and…