Mosaic length and finite interaction-range effects in a one dimensional random energy model

Silvio Franz 1, Giorgio Parisi 2, 3, 4, Federico Ricci-Tersenghi 2

Journal of Physics A: Mathematical and General 41 (2007) 324011

In this paper we study finite interaction range corrections to the mosaic picture of the glass transition as emerges from the study of the Kac limit of large interaction range for disordered models. To this aim we consider point to set correlation functions, or overlaps, in a one dimensional random energy model as a function of the range of interaction. In the Kac limit, the mosaic length defines a sharp first order transition separating a high overlap phase from a low overlap one. Correspondingly we find that overlap curves as a function of the window size and different finite interaction ranges cross roughly at the mosaic lenght. Nonetheless we find very slow convergence to the Kac limit and we discuss why this could be a problem for measuring the mosaic lenght in realistic models.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. Dipartimento di Fisica and INFM,
    Università degli studi di Roma I - La Sapienza
  • 3. Dipartimento di Fisica, SMC, INFM, and INFN,
    Università degli studi di Roma I - La Sapienza
  • 4. Dipartimento di Fisica, Sezione INFN, SMC and UdRm1 of INFM,
    Università degli studi di Roma I - La Sapienza