Energy trapped Ising model

In this paper we have considered the 3D Ising model perturbed with the energy operator coupled with a nonuniform harmonic potential acting as a trap, showing that this system satisfies the trap-size scaling behavior. Eventually, we have computed the correlators $⟨\sigma (z)\sigma (0)⟩$, $⟨\epsilon (z)\epsilon (0)⟩$ and $⟨\sigma (z)\epsilon (0)⟩$ near the critical point by means of conformal perturbation theory. Combining this result with Monte Carlo simulations, we have been able to estimate the OPE coefficients $C_{\sigma \epsilon }^{\sigma }$, $C_{\sigma \sigma }^{\epsilon }$ and $C_{\epsilon \epsilon }^{\epsilon }$, finding a good agreement with the values obtained in [G. Costagliola, Phys. Rev. D 93, 066008 (2016), F. Kos, D. Poland, D. Simmons-Duffin, and A. Vichi, J. High Energy Phys. 08 (2016) 036].

Figure 1

Bi-log plots of the spin (Left panel) and energy (Right panel) one-point functions against power law fits (red line). Due to numerical accuracy, the fits have been performed for values of $\rho$ greater than the ones indicated by the dashed vertical lines.

Figure 2

Results for the spin-spin (left) and energy-energy (right) two-point functions and their fits with the expected behavior [Eqs. (3.12) and (3.13)] red line. Due to numerical accuracy, fits are performed for values of $r$ greater than the ones indicated by the black dashed vertical lines. Error bars are small and usually hidden within the points size.

Figure 3

Fit for the spin-energy two-point function against the theoretically expected behavior performed not including (green line) and including (red line) the second term in Eq. (3.14). As it is evident, the red line agrees consistently better with the numerical result.