Conformal invariance in the nonperturbative renormalization group: A rationale for choosing the regulator

Physical Review. E
Ivan BalogNicolás Wschebor

Abstract

Field-theoretical calculations performed in an approximation scheme often present a spurious dependence of physical quantities on some unphysical parameters associated with the details of the calculation setup (such as the renormalization scheme or, in perturbation theory, the resummation procedure). In the present article, we propose to reduce this dependence by invoking conformal invariance. Using as a benchmark the three-dimensional Ising model, we show that, within the derivative expansion at order 4, performed in the nonperturbative renormalization group formalism, the identity associated with this symmetry is not exactly satisfied. The calculations which best satisfy this identity are shown to yield critical exponents which coincide to a high accuracy with those obtained by the conformal bootstrap. Additionally, this work gives a strong justification to the success of a widely used criterion for fixing the appropriate renormalization scheme, namely the principle of minimal sensitivity.

References

Jun 1, 2004·Physical Review Letters·Léonie CanetNicolas Wschebor
Jul 13, 2004·Physical Review Letters·Léonie CanetBertrand Delamotte
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F BenitezN Wschebor
May 21, 2010·Physical Review Letters·Léonie CanetNicolás Wschebor
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T Machado, N Dupuis
Aug 27, 2011·Physical Review Letters·Matthieu Tissier, Gilles Tarjus
Feb 7, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Léonie CanetNicolás Wschebor
Apr 3, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F BenitezN Wschebor
Nov 28, 2015·Physical Review Letters·F Léonard, B Delamotte
Feb 13, 2016·Physical Review. E·Bertrand DelamotteNicolás Wschebor
Jan 11, 2020·Physical Review Letters·Ivan BalogNicolás Wschebor

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