Thermodynamics of the Lévy spin glass

Details Thermodynamics of the Lévy spin glass Thermodynamics of the Lévy spin glass

2010-06-15

arxiv.org/abs/1006.2927v1

Phys. Rev. E 82, 021127 (2010)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1103/PhysRevE.82.021127

We investigate the L\'evy 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.

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