Boundary operator product expansion coefficients of the three-dimensional Ising universality class

TL;DR

This paper uses Monte Carlo simulations and conformal field theory to accurately determine boundary operator product expansion coefficients and surface scaling dimensions in the 3D Ising universality class with surfaces.

Contribution

It provides the first high-precision estimates of universal boundary OPE coefficients and refines the surface scaling dimension at the special transition in the 3D Ising model.

Findings

Accurate boundary OPE coefficients for the 3D Ising class.

Refined estimate of the surface scaling dimension at the special transition.

Demonstration of combined Monte Carlo and conformal field theory methods.

Abstract

Recent advances in conformal field theory and critical phenomena have focused on the characterization of boundary or defects in a conformally invariant system. In this Letter we study the critical behavior of the three-dimensional Ising universality class in the presence of a surface, realizing the ordinary, the special, and the normal universality classes. By combining high-precision Monte Carlo simulations of an improved model, where leading scaling corrections are suppressed, with a finite-size scaling analysis informed by conformal field theory, we determine unbiased, accurate estimates of universal boundary operator product expansion coefficients of experimental relevance. Furthermore, we improve the value of the scaling dimension of the surface field at the special transition by the estimate $\hat{\Delta}_\sigma = 0.3531(3)$.