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2015

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

Costagliola, Gianluca

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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 $C^{\sigma}_{\sigma\epsilon}= 1.051(3)$ , 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.

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