Related papers: Phases in Large Combinatorial Systems
Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay…
We investigate the emergence of a myriad of phases in the strong coupling regime of the dipolar Hubbard model in two dimensions. By using a combination of numerically unbiased methods in finite systems with analytical perturbative…
The paper is devoted to a study of phase transitions in the Hermitian random matrix models with a polynomial potential. In an alternative equivalent language, we study families of equilibrium measures on the real line in a polynomial…
A phase-separation front will leave in its wake a phase-separated morphology that differs markedly from homogeneous phase-separation morphologies. For a purely diffusive system such a front, moving with constant velocity, will generate very…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
We investigate the phase diagram of a two-component associating fluid mixture in the presence of selectively adsorbing substrates. The mixture is characterized by a bulk phase diagram which displays peculiar features such as closed loops of…
Several models of baryo(lepto)-genesis that give rise to large inhomogeneities in the composition of the universe are presented. In particular, a variation of primordial abundances of light elements by the factor 2-5 at large distances is…
We analyze the existence and the size of the giant component in the stationary state of a Markovian model for bipartite multigraphs, in which the movement of the edge ends on one set of vertices of the bipartite graph is a zero-range…
We construct in the K matrix formalism concrete examples of symmetry enriched topological phases, namely intrinsically topological phases with global symmetries. We focus on the Abelian and non-chiral topological phases and demonstrate by…
Review of selected fundamental topics on the interaction between phase transformations, fracture, and other structural changes in inelastic materials is presented. It mostly focuses on the concepts developed in the author's group over last…
Structural transformations at interfaces are of profound fundamental interest as complex examples of phase transitions in low-dimensional systems. Despite decades of extensive research, no compelling evidence exists for structural…
We discuss the interrelation between phase transitions in interacting lattice or continuum models, and the existence of infinite clusters in suitable random-graph models. In particular, we describe a random-geometric approach to the phase…
Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…
We determine the asymptotic size of the largest component in the $2$-type binomial random graph $G(\mathbf{n},P)$ near criticality using a refined branching process approach. In $G(\mathbf{n},P)$ every vertex has one of two types, the…
We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…
Composition schemes are ubiquitous in combinatorics, statistical mechanics and probability theory. We give a unifying explanation to various phenomena observed in the combinatorial and statistical physics literature in the context…
In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the…