Related papers: Constructing and proving the ground state of a gen…
Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a…
Although many efficient heuristics have been developed to solve binary optimization problems, these typically produce correlated solutions for degenerate problems. Most notably, transverse-field quantum annealing - the heuristic employed in…
Free energy landscapes provide insights into conformational ensembles of biomolecules. In order to analyze these landscapes and elucidate mechanisms underlying conformational changes, there is a need to extract metastable states with…
We propose an efficient approach to accurately finding the ground-state structures in alloys based on the cluster expansion method. In this approach, a small number of candidate ground-state structures are obtained without any information…
An overview is given over the recently developed and now widely used Monte Carlo algorithms with reduced or eliminated critical slowing down. The basic techniques are overrelaxation, cluster algorithms and multigrid methods. With these…
Clustering is a powerful and extensively used data science tool. While clustering is generally thought of as an unsupervised learning technique, there are also supervised variations such as Spath's clusterwise regression that attempt to…
The work presents a simple formalism which proposes an estimate of the ground state energy from a single reference function. It is based on a perturbative expansion but leads to non linear coupled equations. It can be viewed as well as a…
The growing share of intermittent renewable energy sources, storage technologies, and the increasing degree of so-called sector coupling necessitates optimization-based energy system models with high temporal and spatial resolutions, which…
Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search…
We introduce a method based on semidefinite programming that produces rigorous two-sided bounds on ground state energy densities and correlation functions of translation-invariant classical spin models on infinite lattices. In this method,…
On any locally-finite geometry, the stochastic Ising model is known to be contractive when the inverse-temperature $\beta$ is small enough, via classical results of Dobrushin and of Holley in the 1970's. By a general principle proposed by…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
Numerical simulations of critical lattice systems are fundamentally limited by critical slowing down, as long-range correlations are typically established through slow temporal equilibration. A physically constrained generative framework…
We study the Ising model at fixed magnetization on a triangular ladder with three-spin interactions. By recasting the ground-state determination as a linear programming (LP) problem, we solve it exactly using standard LP techniques. We…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
Obtaining the low-energy configurations of spin glasses that have rugged energy landscapes is of direct relevance to combinatorial optimization and fundamental science. Search-based heuristics have difficulty with this task due to the…
In this paper, we study the problem of finding the global minima of a given function. Specifically, we consider complicated functions with numerous local minima, as is often the case for real-world data mining losses. We do so by applying a…
I present a cluster Monte Carlo algorithm that gives direct access to the interface free energy of Ising models. The basic idea is to simulate an ensemble that consists of both configurations with periodic and with antiperiodic boundary…
The antiferromagnetic Ising model on a triangular lattice (AFIT) exemplifies the most classical frustration system, arising from its triangular geometry that prevents all interactions from being simultaneously satisfied. Understanding…