Operator product expansion coefficients of the 3D Ising model with a trapping potential

Recently the operator product expansion coefficients of the 3D Ising model universality class have been calculated by studying via Monte Carlo simulation 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 nonuniform potential acting as a trap. This setting is described by the trap size scaling ansatz, which can be combined with the general framework of the conformal perturbation in order to write down the correlators $⟨\ensuremath{\sigma}(\mathbf{r})\ensuremath{\sigma}(0)⟩$, $⟨\ensuremath{\sigma}(\mathbf{r})\ensuremath{\epsilon}(0)⟩$ and $⟨\ensuremath{\epsilon}(\mathbf{r})\ensuremath{\epsilon}(0)⟩$, from which the operator product expansion coefficients can be estimated. We find ${C}_{\ensuremath{\sigma}\ensuremath{\epsilon}}^{\ensuremath{\sigma}}=1.051(3)$, in agreement with the results already known in the literature, and ${C}_{\ensuremath{\epsilon}\ensuremath{\epsilon}}^{\ensuremath{\epsilon}}=1.32(15)$, confirming and improving the previous estimate obtained in the uniform perturbation case.