Journal of Statistical Physics

, Volume 162, Issue 1, pp 1–42 | Cite as

Structure of Finite-RSB Asymptotic Gibbs Measures in the Diluted Spin Glass Models



We suggest a possible approach to proving the Mézard–Parisi formula for the free energy in the diluted spin glass models, such as diluted K-spin or random K-sat model at any positive temperature. In the main contribution of the paper, we show that a certain small modification of the Hamiltonian in any of these models forces all finite-RSB asymptotic Gibbs measures in the sense of the overlaps to satisfy the Mézard–Parisi ansatz for the distribution of spins. Unfortunately, what is still missing is a description of the general full-RSB asymptotic Gibbs measures. If one could show that the general case can be approximated by finite-RSB case in the right sense then one could a posteriori remove the small modification of the Hamiltonian to recover the Mézard–Parisi formula for the original model.


Spin glasses Diluted models Free energy 

Mathematics Subject Classification

60K35 60G09 82B44 



Dmitry Panchenko is partially supported by NSERC grant.


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Deparment of MathematicsUniversity of TorontoTorontoCanada

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