Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

@article{Guerra2003BrokenRS,
  title={Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model},
  author={Francesco Guerra},
  journal={Communications in Mathematical Physics},
  year={2003},
  volume={233},
  pages={1-12}
}
  • F. Guerra
  • Published 7 May 2002
  • Mathematics
  • Communications in Mathematical Physics
Abstract: By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend this argument in order to compare the limiting free energy with the expression given by the Parisi Ansatz, and including full spontaneous replica symmetry breaking. Our main result is that the quenched average of the free energy is bounded from… 

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TLDR
This analysis is an adaption of a “conditional quenched equals annealed” argument used by Bolthausen to analyze the high-temperature regime of the Sherrington-Kirkpatrick model.
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