OPE Coefficients of the 3D Ising model with a trapping potential

Abstract

Recently the OPE coefficients of the 3D Ising model universality class have been calculated by studying the two-point functions perturbed from the critical point with a relevant field. We show that this method can be applied also when the perturbation is performed with a relevant field coupled to a non uniform potential acting as a trap. This setting is described by the trap size scaling ansatz, that can be combined with the general framework of the conformal perturbation in order to write down the correlators $<\sigma (\mathbf{r})\sigma (0)>$, $<\sigma (\mathbf{r})\epsilon (0)>$ and $<\epsilon (\mathbf{r})\epsilon (0)>$, from which the OPE coefficients can be estimated. We find $C_{\sigma \epsilon }^{\sigma }=1.051(3)$ , in agreement with the results already known in the literature, and $C_{\epsilon \epsilon }^{\epsilon }=1.32(15)$ , confirming and improving the previous estimate obtained in the uniform perturbation case.

6 pages, 4 figures

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Bootstrapping the O(N) Vector Models
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bounds on 4D Conformal and Superconformal Field Theories
• More constraining conformal bootstrap
• Bootstrapping the 3d Ising twist defect
• Critical Behavior of a Trapped Interacting Bose Gas
• Conformal Field Theories in Fractional Dimensions
• Central Charge Bounds in 4D Conformal Field Theory
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators
• Finite-size scaling behavior in trapped systems
• Universal scaling of three-dimensional bosonic gases in a trapping potential

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• 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
• 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