The Sherrington-Kirkpatrick Model: An Overview

@article{Panchenko2012TheSM,
  title={The Sherrington-Kirkpatrick Model: An Overview},
  author={Dmitry Panchenko},
  journal={Journal of Statistical Physics},
  year={2012},
  volume={149},
  pages={362-383}
}
  • D. Panchenko
  • Published 2012
  • Computer Science, Physics, Mathematics
  • Journal of Statistical Physics
The goal of this paper is to review some of the main ideas that emerged from the attempts to confirm mathematically the predictions of the celebrated Parisi ansatz in the Sherrington-Kirkpatrick model. We try to focus on the big picture while sketching the proofs of only a few selected results, but an interested reader can find most of the missing details in Panchenko (The Sherrington-Kirkpatrick Model, Manuscript, 2012) and Talagrand (Mean-Field Models for Spin Glasses, Springer, Berlin, 2011… Expand

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References

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The recent proof by Guerra that the Parisi ansatz provides a lower bound on the free energy of the Sherringtun-Kirkpatrick (SK) spin-glass model could have been taken as offering some support to theExpand
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Abstract It was already clear to Sherrington and Kirkpatrick [Phys. Rev. B 17 (1978) 4384–4403] that the limiting free energy in Sherrington–Kirkpatrick's Spin Glass Model does not depend on theExpand
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In this chapter we prove the Parisi formula, which gives the limiting value of the free energy per site for the Sherrington-Kirkpatrick model at each temperature, starting with the famous result ofExpand
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AbstractWe prove that ifĤNis the Sherrington-Kirkpatrick (SK) Hamiltonian and the quantity $$\bar q_N = N^{ - 1} \sum \left\langle {S_l } \right\rangle _H^2 $$ converges in the variance to aExpand
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Preface.- 1 The Free Energy and Gibbs Measure.- 2 The Ruelle Probability Cascades.- 3 The Parisi Formula.- 4 Toward a Generalized Parisi Ansatz.- A Appendix.- Bibliography.- Notes and Comments.-Expand
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