Related papers: Correlation functions for the Z-invariant Ising mo…

The form factor bootstrap approach is used to compute the exact contributions in the large distance expansion of the correlation function $<\sigma(x) \sigma(0)>$ of the two-dimensional Ising model in a magnetic field at $T=T_c$. The matrix…

In this work, we exploit the operator content of the $(D_{4}, A_{6})$ conformal algebra. By constructing a $Z_{2}$-invariants fusion rules of a chosen subalgebra and by resolving the bootstrap equations consistent with these rules, we…

We extend the well-known method of calculating bulk correlation functions of the conformal Ising model via bosonisation to situations with boundaries. Oshikawa and Affleck have found the boundary states of two decoupled Ising models in…

Taking the XXZ chain as the main example, we give a review of an algebraic representation of correlation functions in integrable spin chains obtained recently. We rewrite the previous formulas in a form which works equally well for the…

We analyze wavefunctions of the six-vertex model by extending the Izergin-Korepin analysis on the domain wall boundary partition functions. We particularly focus on the case with triangular boundary. By using the $U_q(sl_2)$ $R$-matrix and…

We consider correlation functions of topologically twisted, $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge group ${\rm SU}(2)$ and $N_f\leq 3$ massive hypermultiplets in the fundamental representation. For a smooth, compact,…

We suggest a method to compute the correlation functions in conformal quantum mechanics (CFT$_1$) for the fields that transform under a non-local representation of $\mathfrak{sl}(2)$ basing on the invariance properties. Explicit…

We present a new computational method to calculate arbitrary pair correlation functions of an orthorombic system in the most efficient way. The algorithm is demonstrated by the calculation of the radial distribution function of shock…

Correlation functions of the composite field $T\bar{T}$ in the scaling Lee--Yang model are studied. Using the analytic expression for form factors of this operator recently proposed by Delfino and Niccoli \cite{DN}, we show numerically that…

We consider the one-dimensional random field Ising model, where the spin-spin coupling, $J$, is ferromagnetic and the external field is chosen to be $+h$ with probability $p$ and $-h$ with probability $1-p$. At zero temperature, we…

The n-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over Gelfand-Tzetlin table; integrand (for generic n) is given by linear exponential times rational function. For $n=2$ and…

We study pair correlations in cooperative systems placed on complex networks. We show that usually in these systems, the correlations between two interacting objects (e.g., spins), separated by a distance $\ell$, decay, on average, faster…

Given a finite rhombus tiling of a polygonal region in the plane, the associated critical $Z$-invariant Ising model is invariant under star-triangle transformations. We give a simple matrix formula describing spin correlations between…

We show that the two-dimensional $\mathbb{Z}_2$ invariant for time-reversal invariant insulators can be formulated in terms of the boundary-condition dependence of the ground state wavefunction for both non-interacting and…

A new functional model for pairs of commuting isometries is described. Intertwining operators between such models are then studied in order to approach the classification of invariant subspaces of such pairs.

We show that methods developed in the context of perturbative calculations can be transferred to non-perturbative calculations. We demonstrate that correlation functions on the lattice can be computed with the method of differential…

The energy-energy correlation function of the two-dimensional Ising model with weakly fluctuating random bonds is evaluated in the large scale limit. Two correlation lengths exist in contrast to one correlation length in the pure 2D Ising…

The finite XXZ model with boundaries is considered. We use the Matrix Product Ansatz (MPA), which was originally developed in the studies on the asymmetric simple exclusion process and the quantum antiferromagnetic spin chain. The MPA tells…

(Chern--Simons) vector models exhibit an infinite-dimensional symmetry, the slightly-broken higher-spin symmetry with the unbroken higher-spin symmetry being the first approximation. In this note, we compute the $n$-point correlation…

We derive explicit expressions for the conformal blocks of the Ising conformal field theory, for the correlators of an arbitrary number of primary fields. These results are obtained from the bosonized description of the Ising model.…