Related papers: Efficient simulation of the random-cluster model
Numerical simulations on the total mass, the numbers of bonds on the hull, external perimeter, singly connected bonds and gates into large fjords of the Fortuin-Kasteleyn clusters for two-dimensional q-state Potts models at criticality are…
The two-dimensional Potts model can be studied either in terms of the original Q-component spins, or in the geometrical reformulation via Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for arbitrary real values of…
We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to non-integer…
Fast and accurate optimization and simulation is widely becoming a necessity for large scale transmission resiliency and planning studies such as N-1 SCOPF, batch contingency solvers, and stochastic power flow. Current commercial tools,…
Monte Carlo algorithms, like the Swendsen-Wang and invaded-cluster, sample the Ising and Potts models asymptotically faster than single-spin Glauber dynamics do. Here, we generalize both algorithms to sample Potts lattice gauge theory by…
Spin glasses are notoriously difficult to study both analytically and numerically due to the presence of frustration and metastability. Their highly non-convex landscapes require collective updates to explore efficiently. Currently, most…
We introduce a natural way to extend celebrated spin-cluster Monte Carlo algorithms for fast thermal lattice simulations at criticality, like Wolff, to systems in arbitrary fields, be they linear magnetic vector fields or nonlinear…
When simulating a lattice system near its critical temperature, local algorithms for modeling the system's evolution can introduce very large autocorrelation times into sampled data. This critical slowing down places restrictions on the…
We investigate the simulation methods for a large family of stable random fields that appeared in the recent literature, known as the Karlin stable set-indexed processes. We exploit a new representation and implement the procedure…
The increase in complexity of autonomous systems is accompanied by a need of data-driven development and validation strategies. Advances in computer graphics and cloud clusters have opened the way to massive parallel high fidelity…
We establish a general framework for developing approximation algorithms for a class of counting problems. Our framework is based on the cluster expansion of abstract polymer models formalism of Koteck\'y and Preiss. We apply our framework…
Ising and Potts models can be studied using the Fortuin-Kasteleyn representation through the Edwards-Sokal coupling. This adapts to the setting where the models are exposed to an external field of strength $h>0$. In this representation,…
In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable…
In simulations of some infinite range spin glass systems with finite connectivity, it is found that for any resonable computational time, the saturatedenergy per spin that is achieved by a cluster algorithm is lowered in comparison to that…
Multi-component polymer systems are of interest in organic photovoltaic and drug delivery applications, among others where diverse morphologies influence performance. An improved understanding of morphology classification, driven by…
The computation required for a switching Kalman Filter (SKF) increases exponentially with the number of system operation modes. In this paper, a computationally tractable graph representation is proposed for a switching linear dynamic…
The generalization of Kasteleyn and Fortuin clusters formalism is introduced in XY (or more generally O(n)) models. Clusters geometrical structure may be linked to spin physical properties as correlation functions. To investigate…
We propose a new algorithm for k-means clustering in a distributed setting, where the data is distributed across many machines, and a coordinator communicates with these machines to calculate the output clustering. Our algorithm guarantees…
We construct an efficient cluster algorithm for ferromagnetic SU(N)-symmetric quantum spin systems. Such systems provide a new regularization for CP(N-1) models in the framework of D-theory, which is an alternative non-perturbative approach…
Clustering is a fundamental collective phenomenon in agent-based models (ABMs) of opinion dynamics. To study clustering in systems with co-evolving social and opinion variables, we derive stochastic partial differential equation (SPDE)…