Related papers: The Direct-Connectedness Function in the Random Co…
We study the correlations of pairs of complex logarithms of $\mathbb Z$-lattice points in the complex line at various scalings, proving the existence of pair correlation functions. We prove that at the linear scaling, the pair correlations…
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and for the first time the exact density-to-wavefunction map that underly the…
The k-neighbor graph is a directed percolation model on the hypercubic lattice Z d in which each vertex independently picks exactly k of its 2d nearest neighbors at random, and we open directed edges towards those. We prove that the…
We consider Bernoulli percolation on transitive graphs of polynomial growth. In the subcritical regime ($p<p_c$), it is well known that the connection probabilities decay exponentially fast. In the present paper, we study the supercritical…
This thesis explores the evolution of liquid-state theories based on the Ornstein-Zernike (OZ) equation, summarizing the foundational methods developed by Baxter, Lebowitz, Wertheim, and others. A unifying feature of these approaches is…
We introduce a new paradigm for finite and infinite strict-one-dimensional uniform electron gases. In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. In the high-density limit (small-$r_s$, where…
We study the effects of mobility on two crucial characteristics in multi-scale dynamic networks: percolation and connection times. Our analysis provides insights into the question, to what extent long-time averages are well-approximated by…
We introduce an approximation to the short-range correlation energy functional with multide-terminantal reference involved in a variant of range-separated density-functional theory. This approximation is a local functional of the density,…
The random percolation model can be viewed as the dual of a well defined confining gauge theory; since this theory, having no Monte Carlo dynamics at all, is simple to simulate, it is possible to study the properties of the flux tube with…
We consider spread-out models of self-avoiding walk, bond percolation, lattice trees and bond lattice animals on the d-dimensional hyper cubic lattice having long finite-range connections, above their upper critical dimensions d=4…
For the three-dimensional hard-sphere model we investigate the inhomogeneous two-body correlations predicted by Rosenfeld's fundamental measure theory. For the special cases in which the density has either planar or spherical symmetry we…
We give an introductory account of the recent hyperdensity functional theory for the equilibrium statistical mechanics of soft matter systems [F. Samm\"uller et al., Phys. Rev. Lett. 133, 098201 (2024); 10.1103/PhysRevLett.133.098201].…
We establish the sharpness of the percolation phase transition for a class of infinite-range weighted random connection models. The vertex set is given by a marked Poisson point process on $\mathbb{R}^d$ with intensity $\lambda>0$, where…
We derive an energy-based continuum limit for $\varepsilon$-graphs endowed with a general connectivity functional. We prove that the discrete energy and its continuum counterpart differ by at most $O(\varepsilon)$; the prefactor involves…
The correlation function of two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor representation are…
In arXiv:1911.08172 we have studied the single-particle free energy of a class of Little String Theories of A-type, which are engineered by $N$ parallel M5-branes on a circle. To leading instanton order (from the perspective of the low…
We have studied the structure and thermodynamic properties of isotropic three-dimensional core-softened fluid by using the second-order Ornstein-Zernike integral equations completed by the hypernetted chain and Percus-Yevick closures. The…
We study an asymptotic expansion of the critical point for the nearest-neighbor oriented percolation on $\mathbb Z^d$ in powers of $d^{-1}$ as $d\rightarrow \infty$. The proof relies heavily on the lace expansion.
We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory…
A new approach to modelling the behaviour of simple fluids is presented. Starting from the usual expression of the partition function of N molecules, a Fourier transformation is performed. It is argued that the N(N-1)/2 dynamical variables…