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 $<\sigma (\mathbf{r})\sigma (0)>$, $<\sigma (\mathbf{r})ϵ(0)>$ and $<ϵ(\mathbf{r})ϵ(0)>$, from which the OPE coefficients can be estimated. We find $C_{\sigma ϵ}^{\sigma }=1.051(3)$ , in agreement with the results already known in the literature, and $C_{ϵϵ}^{ϵ}=1.32(15)$ , confirming and improving the previous estimate obtained in the uniform perturbation case.

Comments: 6 pages, 4 figures