Scale invariance implies conformal invariance for the three-dimensional Ising model

Understand

Using Wilson renormalization group, we show that if no integrated vector operator of scaling dimension $-1$ exists, then scale invariance implies conformal invariance.

• By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class.
• This shows, in particular, that scale invariance implies conformal invariance for the three-dimensional Ising model.