Related papers: On two-point boundary correlations in the six-vert…
In two-dimensional statistical physics, correlation functions of the O(N) and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as…
Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in three- and four-dimensional conformal…
Two-dimensional $CP^{N-1}$ models are investigated by Monte Carlo methods on the lattice, for values of $N$ ranging from 2 to 21. Scaling and rotation invariance are studied by comparing different definitions of correlation length $\xi$.…
The two-point correlation function is calculated in the Lorentzian EPRL spinfoam model, and shown to match with the one in Regge calculus in a proper limit: large boundary spins, and small Barbero-Immirzi parameter, keeping the size of the…
We obtain explicit expressions for the long range correlations in the ABC model and in diffusive models conditioned to produce an atypical current of particles.In both cases, the two-point correlation functions allow to detect the…
We study various correlation functions (two and three point functions) in a large $N$ matrix model of six commuting matrices with a numerical Monte Carlo algorithm. This is equivalent to a model of a gas of particles in six dimensions with…
Conjectures for analytical expressions for correlations in the dense O$(1)$ loop model on semi infinite square lattices are given. We have obtained these results for four types of boundary conditions. Periodic and reflecting boundary…
We define a new family of overlaps $C_{N,m}$ for the XXZ Hamiltonian on a periodic chain of length $N$. These are equal to the linear sums of the groundstate components, in the canonical basis, wherein $m$ consecutive spins are fixed to the…
We study the XY model on a lattice with fluctuating connectivity. The expectation is that at an appropriate critical point such a system corresponds to a compactified boson coupled to 2d quantum gravity. Our simulations focus, in…
Correlation functions and form factors in vertex models or spin chains are known to satisfy certain difference equations called the quantum Knizhnik-Zamolodchikov equations. We find similar difference equations for the case of semi-infinite…
In this letter, the 6-vertex model on dynamical random lattices is defined via a matrix model and rewritten (following I. Kostov) as a deformation of the O(2) model. In the large N planar limit, an exact solution is found at criticality.…
We address the question of the dependence of the bulk free energy on boundary conditions for the six vertex model. Here we compare the bulk free energy for periodic and domain wall boundary conditions. Using a determinant representation for…
We obtain asymptotic formulae with optimal error terms for the number of lattice points under and near a dilation of the standard parabola, the former improving upon an old result of Popov. These results can be regarded as achieving the…
Totally asymmetric simple exclusion processes on lattices with junctions, where particles interact with hard-core exclusion and move on parallel lattice branches that at the junction combine into a single lattice segment, are investigated.…
We explore how matrix bootstrap techniques can be used to constrain matrix and tensor models at finite $N$, where $N$ is the dimension of the matrix/tensor, taking a Gaussian model with a quartic interaction as example. For matrix models,…
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…
We discuss in this paper combinatorial aspects of boundary loop models, that is models of self-avoiding loops on a strip where loops get different weights depending on whether they touch the left, the right, both or no boundary. These…
We consider near-critical two-dimensional statistical systems with boundary conditions inducing phase separation on the strip. By exploiting low-energy properties of two-dimensional field theories, we compute arbitrary $n$-point correlation…
We develop the idea that a natural link between Boltzmann schemes and finite volumes exists naturally: the conserved mass and momentum during the collision phase of the Boltzmann scheme induces general expressions for mass and momentum…
We show that in boundary CFTs, there exists a one-to-one correspondence between the boundary operator expansion of the two-point correlation function and a power series expansion of the layer susceptibility. This general property allows the…