Renormalization and quantum scaling of Frenkel-Kontorova models

Nuno R Catarino, Robert S. MacKay

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We generalise the classical Transition by Breaking of Analyticity for the class of Frenkel-Kontorova models studied by Aubry and others to non-zero Planck's constant and temperature. This analysis is based on the study of a renormalization operator for the case of irrational mean spacing using Feynman's functional integral approach. We show how existing classical results extend to the quantum regime. In particular we extend MacKay's renormalization approach for the classical statistical mechanics to deduce scaling of low frequency effects and quantum effects. Our approach extends the phenomenon of hierarchical melting studied by Vallet, Schilling and Aubry to the quantum regime. © 2005 Springer Science+Business Media, Inc.

Original languageEnglish
Pages (from-to)995-1014
Number of pages20
JournalJournal of Statistical Physics
Issue number5-6
Publication statusPublished - Dec 2005


  • Quantum scaling specific heat
  • Renormalization
  • Transition by breaking of analyticity


Dive into the research topics of 'Renormalization and quantum scaling of Frenkel-Kontorova models'. Together they form a unique fingerprint.

Cite this