Field theory guides Monte Carlo in the one-dimensional long-range Ising model

Abstract: The statistical long-range Ising (LRI) model in one dimension provides a family of some of the simplest non-exactly solvable critical points. These critical points are described by long-range conformal field theories (CFTs) that are well understood analytically with perturbative expansions and some exact results. Guided by this, we revisit the Monte Carlo (MC) approach to the corresponding lattice model which has many favorable features compared to other systems studied with MC methods. In particular, with very modest computational cost, we are able to estimate scaling dimensions of leading and subleading operators as well as the associated three-point functions, and even certain four-point functions. These results help highlight the fact that 1d LRI CFTs are a phenomenal playground to more generally test non-perturbative methods and ideas for strongly coupled CFTs.