# Thermodynamics of the Lévy spin glass

### K. Janzen 1, A. Engel 2, M. Mézard 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 82 (2010) 021127

We investigate the Lévy glass, a mean-field spin glass model with power-law distributed couplings characterized by a divergent second moment. By combining extensively many small couplings with a spare random backbone of strong bonds the model is intermediate between the Sherrington-Kirkpatrick and the Viana-Bray model. A truncated version where couplings smaller than some threshold $\eps$ are neglected can be studied within the cavity method developed for spin glasses on locally tree-like random graphs. By performing the limit $\eps\to 0$ in a well-defined way we calculate the thermodynamic functions within replica symmetry and determine the de Almeida-Thouless line in the presence of an external magnetic field. Contrary to previous findings we show that there is no replica-symmetric spin glass phase. Moreover we determine the leading corrections to the ground-state energy within one-step replica symmetry breaking. The effects due to the breaking of replica symmetry appear to be small in accordance with the intuitive picture that a few strong bonds per spin reduce the degree of frustration in the system.

• 1. Institut für Physik,
Carl von Ossietzky Universität
• 2. Institut für Physik,
Carl-von-Ossietzky-Universität
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud