arXiv subjects

Evan K. Owen

Publications and source records attributed to Evan K. Owen.

3 recordsLinked to original sources

arXiv2024

The Ising Model on $\mathbb S^2$

We define a 2-dimensional Ising model on a triangulated sphere, $\mathbb S^2$, designed to approach the exact conformal field theory (CFT) in the continuum limit. Surprisingly, the derivation leads to a set of geometric constraints that the lattice field theory must satisfy. Monte Carlo simulations are in agreement with the exact Ising CFT on $\mathbb S^2$. We discuss the inherent benefits of using non-uniform simplicial lattices and how these methods may be generalized for use with other quantum theories on curved manifolds.

hep-lat↗

arXiv2023

The Operator Product Expansion for Radial Lattice Quantization of 3D $ϕ^4$ 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 $ϕ^4$ 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 $Δ_ε$ and $Δ_{T}$ as well as ratios of the operator product expansion (OPE) coefficients $f_{σσε}$ and $f_{σσT}$ of the first spin-0 and spin-2 primary operators $ε$ and $T$ of the 3d Ising CFT.

hep-lat↗

arXiv2022

Ising Model on the Affine Plane

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 by introducing a metric on the lattice through the map $\sinh(2K_i) = \ell^*_i/ \ell_i$ which relates critical couplings to the ratio of the dual hexagonal and triangular edge lengths. Applied to a 2d toroidal lattice, this provides an exact lattice formulation in the continuum limit to the Ising CFT as a function of the modular parameter. This example can be viewed as a quantum generalization of the finite element method (FEM) applied to the strong coupling CFT at a Wilson-Fisher IR fixed point and suggests a new approach to conformal field theory on curved manifolds based on a synthesis of simplicial geometry and projective geometry on the tangent planes.

hep-th↗