Related papers: Sharp Phase Transitions for k-Fold Coverage Using …

Let $Y\subseteq \mathbb{R}^n$ be a closed definable subset and $X\subseteq \mathbb{R}^n$ be a smooth manifold. We construct a version of Morse theory for the restriction to $X$ of the Euclidean distance function from $Y$. This is done using…

We consider tensor factorizations using a generative model and a Bayesian approach. We compute rigorously the mutual information, the Minimal Mean Squared Error (MMSE), and unveil information-theoretic phase transitions. In addition, we…

Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable…

We apply the fidelity metric approach to analyze two recently introduced models that exhibit a quantum phase transition to a topologically ordered phase. These quantum models have a known connection to classical statistical mechanical…

We present a new theoretical approach for the study of the phase diagram of interacting quantum particles: bosons, fermions or spins. In the neighborhood of a phase transition, the expected renormalization group structure is recovered both…

Weakly stationary random processes of $k$-dimensional affine subspaces (flats) in $\mathbb{R}^n$ are considered. If $2k\geq n$, then intersection processes are investigated, while in the complementary case $2k<n$ a proximity process is…

Core decomposition is a classic technique for discovering densely connected regions in a graph with large range of applications. Formally, a $k$-core is a maximal subgraph where each vertex has at least $k$ neighbors. A natural extension of…

We study the survival/extinction phase transition for contact processes with quenched disorder. The disorder is given by a locally finite random graph with vertices indexed by the integers that is assumed to be invariant under index shifts…

We study an effective theory for QCD at finite temperature and density which contains the leading center symmetric and center symmetry breaking terms. The effective theory is studied in a flux representation where the complex phase problem…

Using machine learning (ML) to recognize different phases of matter and to infer the entire phase diagram has proven to be an effective tool given a large dataset. In our previous proposals, we have successfully explored phase transitions…

We propose a method to determine the quantum phase boundaries of one-dimensional systems using sine-square deformation (SSD). Based on the proposition, supported by several exactly solved cases though not proven in full generality, that "if…

Ptychography is an imaging technique which involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the…

In this note we study the phase transition for percolation on quasi-transitive graphs with quasi-transitively inhomogeneous edge-retention probabilities. A quasi-transitive graph is an infinite graph with finitely many different "types" of…

By using our novel Grassmann formulation we study the phase transition of the spanning-hyperforest model of the k-uniform complete hypergraph for any k>= 2. The case k=2 reduces to the spanning-forest model on the complete graph. Different…

We demonstrate the identification and classification of topological phase transitions from experimental data using Diffusion Maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system…

A local criterion of topological phase transitions is established based on the Morse theory: a topological phase transition occurs when the count of Morse critical points of the order function changes. The locations in space where this…

Consider the noisy underdetermined system of linear equations: y=Ax0 + z0, with n x N measurement matrix A, n < N, and Gaussian white noise z0 ~ N(0,\sigma^2 I). Both y and A are known, both x0 and z0 are unknown, and we seek an…

Spin-boson models are essentially useful in the understanding of quantum optics, nuclear physics, quantum dissipation, and quantum computation. We discuss quantum phase transitions in various spin-boson Hamiltonians, compare, and contrast…

We are interested in phase transitions in certain percolation models on point processes and their dependence on clustering properties of the point processes. We show that point processes with smaller void probabilities and factorial moment…

Given a $k$-uniform hyper-graph, the E$k$-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyper-edge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to…