Related papers: The Direct-Connectedness Function in the Random Co…
We derive precise Ornstein-Zernike asymptotic formula for the decay of the two-point function in the general context of finite range Ising type models on Z^d. The proof relies in an essential way on the a-priori knowledge of the strict…
Loop percolation, also known as the dense O(1) loop model, is a variant of critical bond percolation in the square lattice Z^2 whose graph structure consists of a disjoint union of cycles. We study its connectivity pattern, which is a…
We develop a free energy functional for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function. These correlation functions are found by solving the Ornstein- Zernike…
We consider percolation of the vacant set of random interlacements at intensity $u$ in dimensions three and higher, and derive lower bounds on the truncated two-point function for all values of $u>0$. These bounds are sharp up to principal…
We report on a high temperature perturbation expansion study of the superfluid-density spatial correlation function of a Ginzburg-Landau-model superconducting film in a magnetic field. We have derived a closed form which expresses the…
Consider an anisotropic independent bond percolation model on the $d$-dimensional hypercubic lattice, $d\geq 2$, with parameter $p$. We show that the two point connectivity function $P_{p}(\{(0,\dots,0)\leftrightarrow (n,0,\dots,0)\})$ is a…
A method to obtain (approximate) analytical expressions for the radial distribution functions in a multicomponent mixture of additive hard spheres that was recently introduced is used to obtain the direct correlation functions and bridge…
We develop an Ornstein--Zernike theory for the two-dimensional random-cluster model with $1 \leq q <4$ that also applies in its near-critical regime. In particular, we prove an asymptotic formula for the two-point function which holds…
How can the `affinity' or `strength' of ties of a random graph be characterized and compactly represented? How can concepts like Fourier and inverse-Fourier like transform be developed for graph data? To do so, we introduce a new…
We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely…
We consider the Bernoulli bond percolation process (with parameter $p$) on infinite graphs and we give a general criterion for bounded degree graphs to exhibit a non-trivial percolation threshold based either on a single isoperimetric…
A straightforward expansion of Edwards' functional integral representation of the grand partition function for a polymer liquid as an infinite set of Feynman diagrams is shown to yield a cluster expansion that is closely related to the…
We study site and bond percolation on directed simple random graphs with a given degree distribution and derive the expressions for the critical value of the percolation probability above which the giant strongly connected component emerges…
In real life, networks are dynamic in nature; they grow over time and often exhibit power-law degree sequences. To model the evolving structure of the internet, Barab\'{a}si and Albert introduced a simple dynamic model with a power-law…
We use supervised machine learning together with the concepts of classical density functional theory to investigate the effects of interparticle attraction on the pair structure, thermodynamics, bulk liquid-gas coexistence, and associated…
Using molecular dynamics simulations, we perform the first direct tests of three proposed models for the pair correlation functions of strongly coupled plasmas with species of unequal temperature. The models are all extensions of the…
We derive explicit expressions for dynamical correlations of the field and density operators in the Lieb-Liniger model, within an arbitrary eigenstate with a small particle density ${\cal D}$. They are valid for all space and time and any…
We examine metastable configurations of a two-dimensional system of interacting particles on a quenched random potential landscape and ask how the configurational pair correlation function is related to the particle interactions and the…
The phenomenon of random intensity patterns, for waves propagating in the presence of disorder, is well known in optics and in mesoscopic physics. We study this phenomenon for cold atomic gases expanding, by a diffusion process, in a weak…
The properties of a classical simple liquid can be strongly affected by application of an external potential that supports inhomogeneity. To understand the nature of these property changes the equilibrium particle distribution functions of…