Related papers: 3D Ising Model: a view from the Conformal Bootstra…
We demonstrate that various aspects of Conformal Field Theory are amenable to machine learning. Relatively modest feed-forward neural networks are able to distinguish between scale and conformal invariance of a three-point function and…
We derive a systematic construction for form factors of relevant fields in the thermal perturbation of the tricritical Ising model, an integrable model with scattering amplitudes described by the $E_7$ bootstrap. We find a new type of…
Conformal field theories (CFTs) with MN and tetragonal global symmetry in $d=2+1$ dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions in a wide class of materials. The study of these theories with…
We consider a one-dimensional Ising model in a transverse magnetic field coupled to a dissipative heat bath. The phase diagram and the critical exponents are determined from extensive Monte Carlo simulations. It is shown that the character…
We investigate by Monte Carlo simulations the critical properties of the three-dimensional bond-diluted Ising model. The phase diagram is determined by locating the maxima of the magnetic susceptibility and is compared to mean-field and…
The conformal fixed points of the generalized Thirring model are investigated with the help of bosonization, the large N limit and the operator product expansion. Necessary conditions on the coupling constants for conformal invariance are…
QCD in $d=4-2\epsilon$ space-time dimensions possesses a nontrivial critical point. Scale invariance usually implies conformal symmetry so that there are good reasons to expect that QCD at the critical point restricted to the gauge…
Conformal nets are a mathematical model for conformal field theory, and defects between conformal nets are a model for an interaction or phase transition between two conformal field theories. In the preceding paper of this series, we…
The non-equilibrium phase transition in driven two-dimensional Ising models with two different geometries is investigated using Monte Carlo methods as well as analytical calculations. The models show dissipation through fluctuation induced…
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…
This review aims to offer a pedagogical introduction to the analytic conformal bootstrap program via a journey through selected topics. We review analytic methods which include the large spin perturbation theory, Mellin space methods and…
Predictive inference under a general regression setting is gaining more interest in the big-data era. In terms of going beyond point prediction to develop prediction intervals, two main threads of development are conformal prediction and…
We investigate the application of conformable derivatives to model critical phenomena near continuous phase transitions. By incorporating a deformation parameter into the differential structure, we derive unified expressions for…
A process that images or measures bond energies in the critical Ising model can be in distinct measurement ``phases'', depending on the precision of measurement. We study the transition into the strong-measurement phase using replica field…
We briefly introduce hysteresis in spatially extended systems and the dynamic phase transition observed as the frequency of the oscillating field increases beyond a critical value. Hysteresis and the decay of metastable phases are closely…
We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one…
We provide a brief but self-contained review of two-dimensional conformal field theory, from the basic principles to some of the simplest models. From the representations of the Virasoro algebra on the one hand, and the state-field…
We develop new tools for isolating CFTs using the numerical bootstrap. A "cutting surface" algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale…
We use the correspondence between scalar field theory on $AdS_{d+1}$ and a conformal field theory on $R^d$ to calculate the 3- and 4-point functions of the latter. The classical scalar field theory action is evaluated at tree level.
We consider a conformal field theory in the presence of a boundary, and explain how two-point correlators of mixed bulk-local operators can be bootstrapped by exploiting the analytical structure of the conformal blocks. This yields the…