Comment on "Real-space renormalization-group methods for hierarchical spin glasses"

TL;DR

This paper defends the validity of the Ensemble Renormalization Group (ERG) method for disordered systems, clarifying misconceptions and reaffirming its effectiveness in estimating critical exponents in spin glasses.

Contribution

The authors clarify and defend the ERG method against recent criticisms, reaffirming its accuracy in calculating critical exponents for disordered models.

Findings

ERG method provides accurate critical exponents for spin glasses.

Misinterpretation of finite-size effects led to previous criticisms.

ERG remains a reliable tool when properly applied.

Abstract

In the paper [Angelini M C, Parisi G, and Ricci-Tersenghi F, Ensemble renormalization group for disordered systems, Phys. Rev. B 87 134201 (2013)] we introduced a real-space renormalization group called Ensemble Renormalization Group (ERG) and we applied it to the Edwards-Anderson model, obtaining estimates for the critical exponents in good agreement with those from Monte Carlo simulations. Recently the paper [Castellana M, Real-space renormalization-group methods for hierarchical spin glasses, J. Phys. A: Math. Theor. 52 445002 (2019)] re-examined the ERG method from a different perspective, concluding that the previous results were wrong, and claiming that the ERG method predicts trivially wrong critical exponents. In this comment we explain why the conclusions reached by Castellana are wrong, as they are based on a misinterpretation of finite-size effects. We conclude that the ERG method remains a good RG method to obtain critical exponents in strongly disordered models (if properly used).