Related papers: Multibondic Cluster Algorithm
Given a set of variables and the correlations among them, we develop a method for finding clustering among the variables. The method takes advantage of information implicit in higher-order (not just pairwise) correlations. The idea is to…
We discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model. By using the perspective of probability theory, we detail the nature of a cluster algorithm,…
We study phase-transitions of the ferromagnetic $q$-state Potts chain with random nearest-neighbour couplings having a variance $\Delta^2$ and with homogeneous long-range interactions, which decay with the distance as a power…
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…
We investigate the damage spreading effect in the Fortuin-Kasteleyn random cluster model for 2- and 3-dimensional grids with periodic boundary. For 2D the damage function has a global maximum at $p=\sqrt{q}/(1+\sqrt{q})$ for all $q>0$ and…
We examine a model in which a nonequilibrium phase transition from an active to an extinct state is observed. The order of this phase transition has been shown to be either continuous or first-order, depending on the parameter values and…
We prove that the spectral gap of the Swendsen-Wang dynamics for the random-cluster model is larger than the spectral gap of a single-bond dynamics, that updates only a single edge per step. For this we give a representation of the…
We study the three-point correlation function of the backbone in the two-dimensional $Q$-state Potts model using the Fortuin--Kasteleyn (FK) representation. The backbone is defined as the biconnected skeleton of an FK cluster after removing…
A framework is presented for carrying out simulations of equilibrium systems in the microcanonical ensemble using annealing in an energy ceiling. The framework encompasses an equilibrium version of simulated annealing, population annealing…
We propose a self-adapted Monte Carlo approach to automatically determine the critical temperature by simulating two systems with different sizes at the same temperature. The temperature is increased or decreased by checking the short-time…
We revisit in this paper the problem of connectivity correlations in the Fortuin-Kasteleyn cluster representation of the two-dimensional $Q$-state Potts model conformal field theory. In a recent work [M. Picco, S. Ribault and R.…
I propose a numerical simulation algorithm for statistical systems which combines a microcanonical transfer of energy with global changes in clusters of spins. The advantages of the cluster approach near a critical point augment the speed…
In the realm of big data, discerning patterns in nonlinear systems affected by external control inputs is increasingly challenging. Our approach blends the coarse-graining strengths of centroid-based unsupervised clustering with the clarity…
A spin system is studied, with simultaneous permutation-symmetric Potts and spin-rotation-symmetric clock interactions, in spatial dimensions d=2 and 3. The global phase diagram is calculated from the renormalizaton-group solution with the…
We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their…
Within the framework of imaginary-time evolution for matrix product states, we introduce a cluster version of the infinite time-evolving block decimation algorithm for simulating quantum many-body systems, addressing the computational…
Within the canonical ensemble framework, this paper investigates the presence of higher-order transition signals in the $q$-state Potts model (for $q \geq 3$), using two geometric order parameters: isolated spins number and the average…
We present a fast and robust cluster update algorithm that is especially efficient in implementing the task of image segmentation using the method of superparamagnetic clustering. We apply it to a Potts model with spin interactions that are…
We review the background of the cluster algorithms in Monte Carlo simulation of statistical physics problems. One of the first such successful algorithm was developed by Swendsen and Wang eight years ago. In contrast to the local…
In this work, we discuss the implications of a recently obtained equilibrium fluctuation-dissipation relation on the extension of the available Monte Carlo methods based on the consideration of the Gibbs canonical ensemble to account for…