Energy trapped Ising model

TL;DR

This paper investigates the 3D Ising model under a harmonic trap, demonstrating trap-size scaling, computing correlators via conformal perturbation theory, and estimating OPE coefficients through Monte Carlo simulations.

Contribution

It introduces the analysis of the 3D Ising model with a harmonic trap, combining conformal perturbation theory and Monte Carlo methods to estimate key coefficients.

Findings

Confirmed trap-size scaling behavior in the perturbed Ising model.

Computed correlators near the critical point using conformal perturbation theory.

Estimated OPE coefficients with good agreement to previous results.

Abstract

In this paper we have considered the 3D Ising model perturbed with the energy operator coupled with a non uniform harmonic potential acting as a trap, showing that this system satisfies the trap-size scaling behavior. Eventually, we have computed the correlators $\langle \sigma (z) \sigma (0)\rangle$, $ \langle \epsilon (z) \epsilon (0)\rangle$ and $\langle \sigma (z) \epsilon (0)\rangle$ 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 $C^{\sigma}_{\sigma\epsilon}$, $C^{\epsilon}_{\sigma\sigma}$ and $C^{\epsilon}_{\epsilon\epsilon}$, finding a good agreement with the values obtained in [1,2].