Critical interface: twisting spin glasses at $T_c$

E. Brézin 1, S. Franz 2, G. Parisi 3, 4

Physical Review B 82 (2010) 144427

We consider identical copies of spin glasses in finite dimension coupled at the boundaries. This allows to identify the spin glass analogous of twisted boundary conditions in ferromagnetic system and leads to the definition of an interface free-energy that is positively defined and that should scale with a positive power of the system size in the spin glass phase. In this note we study the behavior of the interface at the spin glass critical temperature $T_c$ within mean field theory. We show that the leading scaling of the interface free-energy does not depend on replica symmetry breaking, and can be obtained by simple scaling arguments using a cubic theory for critical spin glasses.

  • 1. Laboratoire de Physique Théorique de l'ENS (LPTENS),
    CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3. Dipartimento di Fisica,
    “Sapienza” Università di Roma
  • 4. INFM-CNR SMC,
    “Sapienza” Università di Roma, – INFN