期刊
JOURNAL OF STATISTICAL PHYSICS
卷 162, 期 1, 页码 1-42出版社
SPRINGER
DOI: 10.1007/s10955-015-1385-8
关键词
Spin glasses; Diluted models; Free energy
资金
- NSERC
We suggest a possible approach to proving the Mezard-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 Mezard-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 Mezard-Parisi formula for the original model.
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