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

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

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