Journal of Statistical Physics

, Volume 167, Issue 3–4, pp 476–498 | Cite as

Real Space Migdal–Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment

  • Maria Chiara Angelini
  • Giulio Biroli


In this manuscript, in honour of L. Kadanoff, we present recent progress obtained in the description of finite dimensional glassy systems thanks to the Migdal–Kadanoff renormalisation group (MK-RG). We provide a critical assessment of the method, in particular discuss its limitation in describing situations in which an infinite number of pure states might be present, and analyse the MK-RG flow in the limit of infinite dimensions. MK-RG predicts that the spin-glass transition in a field and the glass transition are governed by zero-temperature fixed points of the renormalization group flow. This implies a typical energy scale that grows, approaching the transition, as a power of the correlation length, thus leading to enormously large time-scales as expected from experiments and simulations. These fixed points exist only in dimensions larger than \(d_L>3\) but they nevertheless influence the RG flow below it, in particular in three dimensions. MK-RG thus predicts a similar behavior for spin-glasses in a field and models of glasses and relates it to the presence of avoided critical points.


Renormalization group Glassy systems Spin-Glasses 

Mathematics Subject Classification




We thank C. Cammarota, M. Moore, G. Tarjus, P. Urbani for discussions. We acknowledge support from the ERC Grants NPRGGLASS and from the Simons Foundation (N. 454935, Giulio Biroli).


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Dipartimento di Fisica, Ed. Marconi“Sapienza” Università di RomaRomeItaly
  2. 2.Institut Physique Théorique (IPhT) CEA Saclay, and CNRS URA 2306Gif-Sur-YvetteFrance
  3. 3.Laboratoire de Physique StatistiqueEcole Normale SupérieureParisFrance

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