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

2015/01/31 by Bertrand Delamotte, Matthieu Tissier, Nicolás Wschebor · 1 citation
Mathematics · Physics and Astronomy · #Conformal map #Conformal symmetry #Geometry #Ising model #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Random Matrices and Applications #Renormalization group #Scale invariance #Scaling #Scaling dimension #Statistical physics #Statistics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech #hep-th

paper · pdf · doi:10.1103/physreve.93.012144

published as Phys. Rev. E 93, 012144 (2016) · Phys. Rev. E 93, 012144 (2016)

openalex publication_date 2016/01/25 · arxiv created 2016/01/27 · arxiv updated 2016/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• The renormalization group and the ε expansion
• Infinite conformal symmetry in two-dimensional quantum field theory
• Conformal invariance and bootstrap
• Exact evolution equation for the effective potential
• Ordering, metastability and phase transitions in two-dimensional systems
• The Large N Limit of Superconformal Field Theories and Supergravity
• Conformal Field Theory
• Quantum Physics
• The large N limit of superconformal field theories and supergravity

Cited by

• Ising model [wikipedia]