Related papers: Exact logarithmic four-point functions in the crit…
We derive the boundary four-point Green's functions for conformal loop ensembles (CLE) with $\kappa\in(4,8)$. Specializing to $\kappa=6$ and $\kappa=16/3$, we establish the exact formulas for the boundary four-point connectivities in…
We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip…
In the two-dimensional Ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by extensive Monte Carlo simulations for various strength of disorder. The…
We obtain logarithmic behaviours of a four-point correlation function in the c=-2 conformal field theory by using the Feigin-Fuchs construction. It becomes an indeterminate form by a naive evaluation, but is obtained by introducing an…
We obtain an explicit realization of all the primary fields of the Ising model in terms of a conformal field theory of constrained fermions. The four-point correlators of the energy, order and disorder operators are explicitly calculated.
We use the correspondence between scalar field theory on AdS and induced conformal field theory on its boundary to calculate correlation functions of logarithmic conformal field theory in arbitrary dimensions.Our calculations utilize the…
We study connection probabilities between vertices of the square lattice for the critical random-cluster (FK) model with cluster weight 2, which is related to the critical Ising model. We consider the model on the plane and on domains…
We study four-point functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and non-diagonal combination of representations of the…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
The statistics of critical spin-spin correlation functions in Ising systems with non-frustrated disorder are investigated on a strip geometry, via numerical transfer-matrix techniques. Conformal invariance concepts are used, in order to…
The analysis of correlation function data obtained by Monte Carlo simulations of the two-dimensional 4-state Potts model, XY model, and self-dual disordered Ising model at criticality are presented. We study the logarithmic corrections to…
In conformal field theory (CFT), the four-point correlator is a fundamental object that encodes CFT properties, constrains CFT structures, and connects to the gravitational scattering amplitude in holography theory. However, the four-point…
We consider the supersymmetric approach to gaussian disordered systems like the random bond Ising model and Dirac model with random mass and random potential. These models appeared in particular in the study of the integer quantum Hall…
Field-theoretical calculations predict that, at the upper critical dimension $d_c=4$, the finite-size scaling (FSS) behaviors of the Ising model would be modified by multiplicative logarithmic corrections with thermal and magnetic…
We conjecture an exact form for an universal ratio of four-point cluster connectivities in the critical two-dimensional $Q$-color Potts model. We also provide analogous results for the limit $Q\rightarrow 1$ that corresponds to percolation…
In this paper we investigate the nature of the singularity of the Ising model of the 4-dimensional cubic lattice. It is rigorously known that the specific heat has critical exponent $\alpha=0$ but a non-rigorous field-theory argument…
It is believed that the large-scale geometric properties of two-dimensional critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities…
The intrinsic 4-point coupling, defined in terms of a truncated 4-point function at zero momentum, provides a well-established measure for the interaction strength of a QFT. We show that this coupling can be computed non-perturbatively and…
We perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our…
We demonstrate that the Ising model on a general triangular graph with 3 distinct couplings $K_1,K_2,K_3$ corresponds to an affine transformed conformal field theory (CFT). Full conformal invariance of the $c= 1/2$ minimal CFT is restored…