Thermodynamics of the Lévy spin glass

Abstract

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.

References in corpus (7)

• The Bethe lattice spin glass revisited
• Optimisation problems and replica symmetry breaking in finite connectivity spin-glasses
• The phase diagram of Lévy spin glasses
• Replica structure of one--dimensional Ising models
• Replica theory for Levy spin glasses
• The Levy spin glass transition
• On composite systems of dilute and dense couplings

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