Why the Renormalization Group Is a Good Thing

Maria Chiara Angelini, Giorgio Parisi A, Federico Ricci‐Tersenghi

Abstract In the paper Angelini M C et al (2013 Phys. Rev. B 87 134201) 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 (2019 J. Phys. A: Math. Theor. 52 445002) 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).

Piotr Kielanowski, S. R. Juárez W.

Lothar Schäfer

Nigel D. Goldenfeld

Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.

Adam Rançon, N. Dupuis

We present a nonperturbative renormalization group (RG) approach to the Bose-Hubbard model. By taking as initial condition of the RG flow the (local) limit of decoupled sites, we take into account both local and long-distance fluctuations in a nontrivial way. This approach yields a phase diagram in very good quantitative agreement with the quantum Monte Carlo results and reproduces the two universality classes of the superfluid--Mott-insulator transition with a good estimate of the critical exponents. Furthermore, it reveals the crucial role of the ``Ginzburg length'' as a crossover length between a weakly and a strongly correlated superfluid phase.

James Lawrence Hughes