Exact critical exponents for vector operators in the 3d Ising model and conformal invariance

Understand

It is widely expected that the realization of scale invariance in the critical regime implies conformal invariance for a large class of systems.

• This is known to be true if there exist no integrated operator which transforms like a vector under rotations and which has scaling dimension $-1$.
• In this article we give exact expressions for the critical exponents of some of these vector operators.
• In particular, we show that one operator has scaling dimension exactly 3 in any space dimension.