Related papers: Pair Correlation Functions and a Free-Energy Funct…
We study the Sine$_\beta$ process, the bulk point process scaling limit of beta-ensembles. We provide a representation of its pair correlation function for all $\beta>0$ via a stochastic differential equation. We show that the pair…
We present an explicit momentum space computation of the four-point function of the energy-momentum tensor in 4 spacetime dimensions for the free and conformally invariant theory of a scalar field. The result is obtained by explicit…
The tilted axis cranking model is used in combination with the random phase approximation and particle number projection to analyze the influence of dynamical pair correlations in the high-K bands of 178-W and their effect on relative…
We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves $X(\mathbf{s}_k;t),t\in[0,T],$ observed at spatial locations…
We consider the procedure for calculating the pair correlation function in the context of the Cluster Variation Methods. As specific cases, we study the pair correlation function in the paramagnetic phase of the Ising model with nearest…
Natural orbital functional theory is considered for systems with one or more unpaired electrons. An extension of the Piris natural orbital functional (PNOF) based on electron pairing approach is presented, specifically, we extend the…
Dilute or semi-dilute solutions of non-intersecting self-avoiding walk (SAW) polymer chains are mapped onto a fluid of ``soft'' particles interacting via an effective pair potential between their centers of mass. This mapping is achieved by…
Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic…
Transfer-matrix methods are used to calculate spin-spin correlation functions ($G$), Helmholtz free energies ($f$) and magnetizations ($m$) in the two-dimensional random-field Ising model close to the zero-field bulk critical temperature…
We use the extension of scaled particle theory (ESPT) presented in the accompanying paper [Stillinger et al. J. Chem. Phys. xxx, xxx (2007)] to calculate numerically pair correlation function of the hard sphere fluid over the density range…
We calculate the free energies $F$ for $U(1)$ gauge theories on the $d$ dimensional sphere of radius $R$. For the theory with free Maxwell action we find the exact result as a function of $d$; it contains the term $\frac{d-4}{2} \log R$…
Although the classical density functional theory (DFT) of inhomogeneous fluids was formulated more than four decades ago, its application to broken symmetry phases of molecular systems remained a challenge. Approximate free energy…
We investigate the full pair-distribution function of a homogeneous suspension of spherical active Brownian particles interacting by a Weeks-Chandler-Andersen potential in two spatial dimensions. The full pair-distribution function depends…
In this paper the exact solution and correlation functions for a double-chain Ising model with multi-spin interactions and symmetric Hamiltonian density are obtained. The study employs the transfer matrix method to derive fundamental…
For $0<\theta<1$, we show that for almost all $\alpha$, the pair correlation function of the sequence of fractional parts of $\{\alpha n^\theta:n\geq 1 \}$ is Poissonian.
Particle-particle correlation functions in ionic systems control many of their macroscopic properties. In this work, we use stochastic density functional theory to compute these correlations, and then we analyze their long-range behavior.…
In this article, we study the pair correlation of Farey fractions by proving that the limiting pair correlation function of the sequence of Farey fractions with square-free denominators exists and provide an explicit formula for the…
We extend the formula for correlation functions of free scalar field theories and Dirac field theories in terms of quantum $A_{\infty}$ algebras presented in arXiv:2305.11634 to general scalar-Dirac systems. We obtain the result that the…
The measurements of the magnetic and nematic correlation lengths in a generalization of the two dimensional XY model on the square lattice are presented using classical Monte Carlo simulation. The full phase diagram is re-examined based on…
Simple models for spherical particles with a soft shell have been shown to self-assemble into numerous crystal phases and even quasicrystals. However, most of these models rely on a simple pairwise interaction, which is usually a valid…