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.

arXiv comment4 pages, typos corrected, a few references added

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Cited by in corpus (17)

• Precision Islands in the Ising and $O(N)$ Models
• The Random-Bond Ising Model in 2.01 and 3 Dimensions
• 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
• Conformal perturbation theory
• 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
• OPE Coefficients of the 3D Ising model with a trapping potential
• Conformal perturbation of off-critical correlators in the 3D Ising universality class
• Two- and three-point functions at criticality: Monte Carlo simulations of the three-dimensional $(q+1)$-state clock model
• Conformal perturbation theory confronts lattice results in the vicinity of a critical point
• Numerical estimation of structure constants in the 3d Ising CFT through Markov chain UV sampler
• The Operator Product Expansion for Radial Lattice Quantization of 3D ${\varphi }^4$ Theory
• Energy trapped Ising model
• Critical Three-Dimensional Ising Model on Spheriods from the Conformal Bootstrap
• Operator product expansion coefficients from the nonperturbative functional renormalization group