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Keyword: Sherrington-Kirkpatrick model ×Clear all

2 claims from 1 paper

1. Physics and Astronomy › Theoretical and Computational Physics

   Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

   Guerra · Communications in Mathematical Physics · 2003

   Using an interpolation argument, the paper compares the true free energy of mean field spin glass models with the Parisi Ansatz and shows a lower bound that holds uniformly in system size.

   Unchecked2 claims
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   1. UncheckedFor the Sherrington-Kirkpatrick spin glass, the averaged free energy is bounded below by the Parisi Ansatz value, for every system size.“Our main result is that the quenched average of the free energy is bounded from below by the value given in the Parisi Ansatz uniformly in the size of the system.”
   2. UncheckedThe gap between the true free energy and the Parisi expression is given as a sum rule, extending earlier work on the replica symmetric approximation.“Moreover, the difference between the two expressions is given in the form of a sum rule, extending our previous work on the comparison between the true free energy and its replica symmetric Sherrington-Kirkpatrick approximation.”