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 dL> 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.

Real Space Migdal–Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment / Angelini, Maria Chiara; Biroli, Giulio. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 167:3-4(2017), pp. 476-498. [10.1007/s10955-017-1748-4]

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

Angelini Maria Chiara;
2017

Abstract

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 dL> 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.
2017
Glassy systems; Renormalization group; Spin-Glasses; Statistical and Nonlinear Physics; Mathematical Physics
01 Pubblicazione su rivista::01a Articolo in rivista
Real Space Migdal–Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment / Angelini, Maria Chiara; Biroli, Giulio. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 167:3-4(2017), pp. 476-498. [10.1007/s10955-017-1748-4]
File allegati a questo prodotto
File Dimensione Formato  
Angelini_Real_Space_Migdal_2017.pdf

solo gestori archivio

Tipologia: Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 933.99 kB
Formato Adobe PDF
933.99 kB Adobe PDF   Contatta l'autore

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1167550
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 11
social impact