The 3-dimensional Ising model is a highly important model field theory because many realistic thermodynamic systems - among them all real fluids - are believed to belong to the universality class of this model. (See, e.g., the discussion and references in my paper here.)

The paper under review is an excellent paper, using the relations between conformal field theory and field theories at critical points and newly developed theoretical tools (a variant of the bootstrap program) to calculate the critical exponents of the 3-dimensional Ising model to an accuracy significantly exceeding the previously best calculations (which were obtained by Monte Carlo methods). This shows that the theoretical methods of operator-based quantum field theory are now developed to a very high level.

The techniques are also applied to the 2-dimensional Ising model, which is exactly solvable, with similarly good numerical results.

I already reviewed a companion paper which contains the theoretical results underlying the present paper. I will complete this review in due time by describing the numerical methods, why they work, and what sort of results are obtained. (But because of traveling I must pause for more than week; so be patient.)