Related papers: On two-point boundary correlations in the six-vert…
The trigonometric six-vertex model with domain wall boundary conditions and one partially reflecting end on a lattice of size $2n\times m$, $m\leq n$, is considered. The partition function is computed using the Izergin-Korepin method,…
Recent work in percolation has led to exact solutions for the site and bond critical thresholds of many new lattices. Here we show how these results can be extended to other classes of graphs, significantly increasing the number and variety…
We calculate correlation functions of two local operators within the nucleon carrying momentum. We resolve their dependence on the spatial distance of the currents. This is carried out for all Wick contractions, taking into account several…
We derive the duality symmetries relevant to moduli dependent gauge coupling constant threshold corrections, in Coxeter $ {\bf Z_N} $ orbifolds. We consider those orbifolds for which the point group leaves fixed a 2-dimensional sublattice…
We consider the analogue of the 6-vertex model constructed from alternating spin n/2 and spin m/2 lines, where $1\leq n<m$. We identify the transfer matrix and the space on which it acts in terms of the representation theory of $U_q(sl_2)$.…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
We prove up-to-constants bounds on the two-point function (i.e., point-to-point connection probabilities) for critical long-range percolation on the $d$-dimensional hierarchical lattice. More precisely, we prove that if we connect each pair…
We study the anisotropic boundary conditions for the dilute O(n) loop model with the methods of 2D quantum gravity. We solve the problem exactly on a dynamical lattice using the correspondence with a large $N$ matrix model. We formulate the…
We study the two-boundary extension of a loop model - corresponding to the dense phase of the O(n) model, or to the Q=n^2 state Potts model - in the critical regime -2 < n < 2. This model is defined on an annulus of aspect ratio \tau. Loops…
In solving a system of $n$ linear equations in $d$ variables $Ax=b$, the condition number of the $n,d$ matrix $A$ measures how much errors in the data $b$ affect the solution $x$. Estimates of this type are important in many inverse…
Two-point density-density correlation functions for the diffusive binary reaction system $A+A\to\emptyset$ are obtained in one dimension via Monte Carlo simulation. The long-time behavior of these correlation functions clearly deviates from…
The two-dimensional Ising model is studied at the boundary of a half-infinite cylinder. The three regular lattices (square, triangular and hexagonal) and the three regimes (sub-, super- and critical) are discussed. The probability of having…
It is shown that certain sum rule identities exist which relate correlation functions for $n$ Potts spins on the boundary of a planar lattice for $n\geq 4$. Explicit expressions of the identities are obtained for $n=4,5$. It is also shown…
We consider a quantum two-particle system on a d-dimensional lattice with interaction and in presence of an IID external potential. We establish Wegner-typer estimates for such a model. The main tool used is Stollmann's lemma.
We propose a new way to implement Dirichlet boundary conditions for complex shapes using data from a single node only, in the context of the lattice Boltzmann method. The resulting novel method exhibits second-order convergence for the…
We consider correlation functions in 6d $(2,0)$ theories of two $\frac{1}{2}$-BPS operators inserted away from a $\frac{1}{2}$-BPS surface defect. In the large central charge limit the leading connected contribution corresponds to sums of…
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…
Integrable boundary conditions in 1+1 and 2+1 dimensions are discussed from the higher symmetries point of view. Boundary conditions consistent with the discrete Landau-Lifshitz model and infinite 2D Toda lattice are represented.
We revisit the calculation of height correlations in the two-dimensional Abelian sandpile model by taking advantage of a technique developed recently by Kenyon and Wilson. The formalism requires to equip the usual graph Laplacian,…
In this paper we present a new solution of the star-triangle relation having positive Boltzmann weights. The solution defines an exactly solvable two-dimensional Ising-type (edge interaction) model of statistical mechanics where the local…