Related papers: Graphical representations and cluster algorithms f…
The upper critical dimension of the Ising model is known to be $d_c=4$, above which critical behavior is regarded as trivial. We hereby argue from extensive simulations that, in the random-cluster representation, the Ising model…
The paramagnetic-ferromagnetic transition in the Ising model can be described as percolation of suitably defined clusters. We have tried to extend such picture to the confinement-deconfinement transition of SU(2) pure gauge theory, which is…
The Fortuin-Kasteleyn mapping between the Ising model and the site-bond correlated percolation model is shown to be only one of an infinite class of exact mappings. These new cluster representations are a result of "renormalized"…
Information percolation is a new method for analyzing stochastic spin systems through classifying and controlling the clusters of information-flow in the space-time slab. It yielded sharp mixing estimates (cutoff with an $O(1)$-window) for…
A new cluster algorithm based on invasion percolation is described. The algorithm samples the critical point of a spin system without a priori knowledge of the critical temperature and provides an efficient way to determine the critical…
Clusters and droplets of positive spins in the two-dimensional Ising model percolate at the Curie temperature in absence of external field. The percolative exponents coincide with the magnetic ones for droplets but not for clusters. We use…
The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations…
The fractal structure and scaling properties of a 2d slice of the 3d Ising model is studied using Monte Carlo techniques. The percolation transition of geometric spin (GS) clusters is found to occur at the Curie point, reflecting the…
We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…
Monte Carlo simulations of the 1D Ising model with ferromagnetic interactions decaying with distance $r$ as $1/r^{1+\sigma}$ are performed by applying the Swendsen-Wang cluster algorithm with cumulative probabilities. The critical behavior…
The clusters of up spins of a two-dimensional Ising ferromagnet undergo a second order percolative transition at temperatures above the Curie point. We show that in the scaling limit the percolation threshold is described by an integrable…
Working within the stochastic series expansion framework, we introduce and characterize a new quantum cluster algorithm for quantum Monte Carlo simulations of transverse field Ising models with frustrated Ising exchange interactions. As a…
We report on the development of two dual worm constructions that lead to cluster algorithms for efficient and ergodic Monte Carlo simulations of frustrated Ising models with arbitrary two-spin interactions that extend up to third-neighbours…
The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two…
We demonstrate that the invaded cluster algorithm, recently introduced by Machta et al, is a fast and reliable tool for determining the critical temperature and the magnetic critical exponent of periodic and aperiodic ferromagnetic Ising…
We consider geometrical clusters (i.e. domains of parallel spins) in the square lattice random field Ising model by varying the strength of the Gaussian random field, $\Delta$. In agreement with the conclusion of previous investigation…
A modern graphics processing unit (GPU) is able to perform massively parallel scientific computations at low cost. We extend our implementation of the checkerboard algorithm for the two dimensional Ising model [T. Preis et al., J. Comp.…
Under some general assumptions, we construct the scaling limit of open clusters and their associated counting measures in a class of two dimensional percolation models. Our results apply, in particular, to critical Bernoulli site…
The fractal structure of high-temperature graphs of the three-dimensional Ising and XY models is investigated by simulating these graphs directly on a cubic lattice and analyzing them with the help of percolation observables. The Ising…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…