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

作者：Panchenko Dmitry

来源：Journal of Statistical Physics, 2016, 162(1): 1-42.

DOI：10.1007/s10955-015-1385-8

• Spin glasses
• Diluted models
• Free energy

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.

• 出版日期2016-1