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Results of large-scale Monte Carlo simulations of three-dimensional Ising models with edges and corners are reviewed. At the ordinary transition, angle dependent critical exponents are observed, whereas at the surface transition edge and…
In this paper we present results for bivariate exponential distributions which are represented by phase type distributions. The paper extends results from previous publications [5, 14] on this topic by introducing new representations that…
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…
Experimental quantum simulators have become large and complex enough that discovering new physics from the huge amount of measurement data can be quite challenging, especially when little theoretical understanding of the simulated model is…
We investigate signatures of the excited-state quantum phase transition in the periodic dynamics of the Lipkin-Meshkov-Glick model and the Tavis-Cummings model. In the thermodynamic limit, expectation values of observables in eigenstates of…
A significant generalization of the Erd\"os-R\'enyi random graph model is an `inhomogeneous' random graph where the edge probabilities vary according to vertex types. We identify the threshold value for this random graph with a finite…
We consider single-file diffusion in an open system with two species $A,B$ of particles. At the boundaries we assume different reservoir densities which drive the system into a non-equilibrium steady state. As a model we use an…
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…
In this paper, we develop a two-stage distributed algorithm that enables nodes in a graph to cooperatively estimate the spectrum of a matrix $W$ associated with the graph, which includes the adjacency and Laplacian matrices as special…
We study a non-conserved one-dimensional stochastic process which involves two species of particles $A$ and $B$. The particles diffuse asymmetrically and react in pairs as $A\emptyset\leftrightarrow AA\leftrightarrow BA \leftrightarrow…
We show how averages of exponential functions of path dependent quantities, such as those of Work Fluctuation Theorems, detect phase transitions in deterministic and stochastic systems. State space truncation -- the restriction of the…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…
The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…
Let $\mathbb{S}_g$ be the orientable surface of genus $g$. We prove that the component structure of a graph chosen uniformly at random from the class $\mathcal{S}_g(n,m)$ of all graphs on vertex set $[n]=\{1,\dotsc,n\}$ with $m$ edges…
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…
We study phase transitions in the Ising model on random graphs using graph limits. We show that the critical temperatures are determined by the eigenvalues of the kernel operator associated with the graph limit. Bifurcation diagrams for…
Transitions of many-particle quantum systems between distinct phases at absolute-zero temperature, known as quantum phase transitions, require an exacting treatment of particle correlations. In this work, we present a general…
Two-imcompressible phase model of star is briefly revised. Effects of rotation and general relativity are considered.