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

@article{Delamotte2016ScaleII,
  title={Scale invariance implies conformal invariance for the three-dimensional Ising model.},
  author={Bertrand Delamotte and Matthieu Tissier and Nicol{\'a}s Wschebor},
  journal={Physical review. E},
  year={2016},
  volume={93 1},
  pages={
          012144
        }
}
Using the 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. 

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References

SHOWING 1-10 OF 81 REFERENCES
Quantum Physics: A Functional Integral Point of View
This book is addressed to one problem and to three audiences. The problem is the mathematical structure of modem physics: statistical physics, quantum mechanics, and quantum fields. The unity ofExpand
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)Expand
New York
Table of
Phys
  • Lett. B 335, 364
  • 1994
Commun
  • Math. Phys. 35, 87
  • 1974
Phys
  • Rev. D 91, 021901(R)
  • 2015
Phys. Rev. D
  • Phys. Rev. D
  • 2015
43
  • Fetch the Devil
  • 2014
High Energy Phys
  • High Energy Phys
  • 2014
High Energy Phys
  • High Energy Phys
  • 2014
...
1
2
3
4
5
...