Related papers: On two-point boundary correlations in the six-vert…
It is shown that the partition function of the 2d Ising model on the dual finite lattice with periodical boundary conditions is expressed through some specific combination of the partition functions of the model on the torus with…
Two-particle lattice states are important for physics of magnetism, superconducting oxides, and cold quantum gases. The quantum-mechanical lattice problem is exactly solvable for finite-range interaction potentials. A two-body Schroedinder…
We theoretically explore boundary conditions for lattice Boltzmann methods, focusing on a toy two-velocities scheme to tackle a linear one-dimensional advection equation. By mapping lattice Boltzmann schemes to Finite Difference schemes, we…
We derive the recursive relations of the partition function for the eight-vertex model on an $N\times N$ square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain…
We study numerically the two-point correlation functions of height functions in the six-vertex model with domain wall boundary conditions. The correlation functions and the height functions are computed by the Markov chain Monte-Carlo…
We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions,…
We consider the role of boundary conditions in the $AdS_{d+1}/CFT_{d}$ correspondence for the scalar field theory. Also a careful analysis of some limiting cases is presented. We study three possible types of boundary conditions, Dirichlet,…
The implementation of boundary conditions is among the most challenging parts of modeling fluid flow through channels and complex media. Here, we show that the existing methods to deal with liquid-wall interactions using multicomponent…
The higher rank analogue of the XXZ model with a boundary is considered on the basis of the vertex operator approach. We derive difference equations of the quantum Knizhnik-Zamolodchikov type for 2N-point correlations of the model. We…
This paper is devoted to the 8-vertex model and its edge correlation function. In some particular (integrable) cases, we find a closed form of the edge correlation function and we deduce also its asymptotic. In addition, we quantify…
We study the effect of positive correlations on the critical threshold of site and bond percolation in a square lattice with d = 2. We propose two algorithms for generating dependent lattices with minimal correlation length and non-negative…
The correlation functions of an arbitrary number of boundary monomers in the system of close-packed dimers on the square lattice are computed exactly in the scaling limit. The equivalence of the 2n-point correlation functions with those of…
The connection between matrix integrals and links is used to define matrix models which count alternating tangles in which each closed loop is weighted with a factor n, i.e. may be regarded as decorated with n possible colors. For n=2, the…
A two-body problem on the square lattice is analyzed. The interaction potential consists of strong on-site repulsion and nearest-neighbor attraction. Exact pairing conditions are derived for s-, p-, and d-symmetric bound states. The pairing…
We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of…
The 15-vertex model of Statistical Mechanics is studied on a square domain with partially oriented boundary. With DWBC the model would reduce to the six-vertex model, but more general boundary configurations are available. After…
We calculate the boundary correlation function of fixed-to-free boundary condition changing operators in the square-lattice Ising model. The correlation function is expressed in four different ways using $2\times2$ block Toeplitz…
The six-vertex model is an important toy-model in statistical mechanics for two-dimensional ice with a natural parameter $\Delta$. When $\Delta = 0$, the so-called free-fermion point, the model is in natural correspondence with domino…
We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance…
A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this…