Abstract
Using the Wilson renormalization group, we show that if no integrated vector operator of scaling dimension 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.
- Received 6 January 2015
- Revised 23 October 2015
DOI:https://doi.org/10.1103/PhysRevE.93.012144
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