Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators

Abstract

We propose a general method for the numerical evaluation of OPE coefficients in three dimensional Conformal Field Theories based on the study of the conformal perturbation of two point functions in the vicinity of the critical point. We test our proposal in the three dimensional Ising Model, looking at the magnetic perturbation of the $<\sigma (\mathbf{r})\sigma (0)>$, $<\sigma (\mathbf{r})\epsilon (0)>$ and $<\epsilon (\mathbf{r})\epsilon (0)>$ correlators from which we extract the values of $C_{\sigma \epsilon }^{\sigma }=1.07(3)$ and $C_{\epsilon \epsilon }^{\epsilon }=1.45(30)$. Our estimate for $C_{\sigma \epsilon }^{\sigma }$ agrees with those recently obtained using conformal bootstrap methods, while $C_{\epsilon \epsilon }^{\epsilon }$, as far as we know, is new and could be used to further constrain conformal bootstrap analyses of the 3d Ising universality class.

4 pages, typos corrected, a few references added

References in corpus (6)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bounds on 4D Conformal and Superconformal Field Theories
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Central Charge Bounds in 4D Conformal Field Theory
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap

Cited by in corpus (10)

• A Semidefinite Program Solver for the Conformal Bootstrap
• Operator Product Expansion Coefficients of the 3D Ising Criticality via Quantum Fuzzy Sphere
• Constraining quantum critical dynamics: 2+1D Ising model and beyond
• Fine corrections in the effective string describing SU(2) Yang-Mills theory in three dimensions
• Two- and three-point functions at criticality: Monte Carlo simulations of the improved three-dimensional Blume-Capel model
• Numerical estimation of structure constants in the 3d Ising CFT through Markov chain UV sampler
• Energy trapped Ising model
• The Operator Product Expansion for Radial Lattice Quantization of 3D ${\varphi }^4$ Theory
• Critical Three-Dimensional Ising Model on Spheriods from the Conformal Bootstrap
• Operator product expansion coefficients from the nonperturbative functional renormalization group