Abstract
The authors explore a method for computing correlation functions that is complementary to the well-known bootstrap program and particularly well suited for determining the behavior of off-critical systems, i.e. systems perturbed around their conformal point. They do so for a class of perturbations of the 3$D$ Ising model which are relevant for real experiments on systems in a so-called $t\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l$ $t\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}p$.
Highlights
In recent years, conformal data for several conformal field theories (CFTs) have been determined thanks to the conformal bootstrap program [1,2,3,4,5]
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
In this paper we have further developed the program of studying systems in their off-critical scaling regime, using the consolidated approach based on the operator product expansion (OPE) and the possibility of expanding the Wilson coefficients in terms of the perturbing parameter by means of conformal perturbation theory [6,7,8]
Summary
Conformal data for several conformal field theories (CFTs) have been determined thanks to the conformal bootstrap program [1,2,3,4,5]. In addition to that, combining this numerical high-precision technique to analytical methods developed in the framework of conformal perturbation theory (CPT) [6,7,8], it is possible to determine the behavior of the off-critical correlators of many different systems. This approach has been applied successfully to the well-known 3D Ising model, by adding perturbations proportional to the spin and the energy operator [9,10]. This setup might be implemented in real system experiments and the knowledge of the correlators is fundamental in order to understand the behavior of the observables of this system out of the critical point
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