Strong universality and algebraic scaling in two-dimensional Ising spin glasses

T. Joerg ¹, J. Lukic ¹, E. Marinari ², O. C. Martin ³

Physical Review Letters 96 (2006) 237205

At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but non-zero temperature and provide numerical evidence that $\eta \approx 0$ and $\nu \approx 3.5$ in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds in particular for the $\pm J$ model, with or without dilutions and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T=0, is consistent with a real space renormalization group approach. We also explain how the scaling of the specific heat is compatible with the hyperscaling prediction.

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