Interaction-Flip Identities in Spin Glasses
arXiv:0811.2472 · doi:10.1007/s10955-009-9706-4
Abstract
We study the properties of fluctuation for the free energies and internal energies of two spin glass systems that differ for having some set of interactions flipped. We show that their difference has a variance that grows like the volume of the flipped region. Using a new interpolation method, which extends to the entire circle the standard interpolation technique, we show by integration by parts that the bound imply new overlap identities for the equilibrium state. As a side result the case of the non-interacting random field is analyzed and the triviality of its overlap distribution proved.
To appear on the Brezin-Parisi special issue of Journal of Statistical Physics
References in corpus (7)
- The Thermodynamic Limit in Mean Field Spin Glass Models
- General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity
- On the Stability of the Quenched State in Mean Field Spin Glass Models
- About the overlap distribution in mean field spin glass models
- Spin-Glass Stochastic Stability: a Rigorous Proof
- The infinite volume limit in generalized mean field disordered models
- Replica symmetric spin glass field theory