The Operator Product Expansion for Radial Lattice Quantization of 3D \(\phi^4\) Theory

At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3d Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the Quantum Finite Elements method to implement radially quantized critical \(\phi^4\) theory on simplicial lattices approaching \(\mathbb{R} \times S^2\). Computing the four-point function of identical scalars, we demonstrate the power of radial quantization by the accurate determination of the scaling dimensions \(\Delta_{\epsilon}\) and \(\Delta_{T}\) as well as ratios of the operator product expansion (OPE) coefficients \(f_{\sigma \sigma \epsilon}\) and \(f_{\sigma \sigma T}\) of the first spin-0 and spin-2 primary operators \(\epsilon\) and \(T\) of the 3d Ising CFT.