Related papers: Edge correlation function of the 8-vertex model wh…
We developed a conformal map technique to analyze the attenuation of edge modes propagating along imperfect boundaries. In systems where the potential energy exhibits conformal invariance, the conformal transformation can straighten the…
We study asymptotic behaviour of the correlation functions of bipartite sparse random $N\times N$ matrices. We assume that the graphs have $N$ vertices, the ratio of parts is $\displaystyle\frac{\alpha}{1-\alpha}$ and the average number of…
We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be…
We investigate six types of two-point boundary correlation functions in the dense loop model. These are defined as ratios $Z/Z^0$ of partition functions on the $m\times n$ square lattice, with the boundary condition for $Z$ depending on two…
We analyze the correlation between randomly chosen edge weights on neighboring edges in a directed graph. This shared-endpoint correlation controls the expected organization of randomly drawn edge flows when the flow on each edge is…
We discuss the influence of boundary conditions on the continuum limit of the six-vertex model by deriving a variational principle for the associated height function with arbitrary fixed boundary conditions. We discuss its consequences…
The Kyoto group (Jimbo, Miwa, Nakayashikiet al.) showed that the partition function and correlation funtions of the eight-vertex model in antiferromagnetic phases can be calculated using simple analytical properties of the $R$-matrix. We…
Causal inference has traditionally focused on interventions at the unit level. In many applications, however, the central question concerns the causal effects of connections between units, such as transportation links, social relationships,…
Applying the holographic method, we investigate correlation functions of boundary and defect conformal field theories. To describe boundary conformal field theory, we consider an end of the world brane in an asymptotic AdS space which…
In this paper, we derive cumulant bounds for subgraph counts and power-weighted edge length in a class of spatial random networks known as weighted random connection models. This involves dealing with long-range spatial correlations induced…
We introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the "darkness formation probability" are calculated in the thermodynamical…
Topological phases of matter possess intricate correlation patterns typically probed by entanglement entropies or entanglement spectra. In this work, we propose an alternative approach to assessing topologically induced edge states in free…
We introduce a new family of graphical models that consists of graphs with possibly directed, undirected and bidirected edges but without directed cycles. We show that these models are suitable for representing causal models with additive…
A boundary one point function related to the boundary spontaneous polarization, which is different from the ones considered in the past, is studied for the six vertex model on a 2N \times N lattice with domain wall boundary condition and…
We consider the six-vertex model with reflecting end boundary condition. We compute analytically boundary correlation functions, such as the boundary polarization and the emptiness formation probability. In order to do that, we use the…
The edge-degeneracy model is an exponential random graph model that uses the graph degeneracy, a measure of the graph's connection density, and number of edges in a graph as its sufficient statistics. We show this model is relatively…
As part of our ongoing work on the enumeration of symmetry classes of lozenge tilings of hexagons with certain four-lobed structures removed from their center, we consider the case of the tilings which are both vertically and horizontally…
We introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators. Two examples studied are a two-dimensional second-order topological insulator…
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…
We consider the problem of the exact computation of the correlation functions of the eight-vertex solid-on-solid model by means of the algebraic Bethe Ansatz. We compute the scalar product between a Bethe eigenstate and an arbitrary state…