Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2000-02-22
Eur. Phys. J. B 17, 439-447 (2000)
Physics
Condensed Matter
Disordered Systems and Neural Networks
17 pages, submitted to Euro. Phys. Jou. B Direct
Scientific paper
10.1007/s100510070123
The mean field spin glass model is analyzed by a combination of mathematically rigororous methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural networks. It is well known that the probability measure of overlaps among replicas carries the whole physical content of these models. A functional order parameter of Parisi type is introduced by rigorous methods, according to previous works by F. Guerra. By the Ansatz that the functional order parameter is the correct order parameter of the model, we explicitly find the full overlap distribution. The physical interpretation of the functional order parameter is obtained, and ultrametricity of overlaps is derived as a natural consequence of a branching diffusion process. It is shown by explicit construction that ultrametricity of the 3-replicas overlap distribution together with the Ghirlanda-Guerra relations determines the distribution of overlaps among s replicas, for any s, in terms of the one-overlap distribution.
Baffioni Francesco
Rosati Francesco
No associations
LandOfFree
Some Exact Results on the Ultrametric Overlap Distribution in Mean Field Spin Glass Models (I) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Some Exact Results on the Ultrametric Overlap Distribution in Mean Field Spin Glass Models (I), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some Exact Results on the Ultrametric Overlap Distribution in Mean Field Spin Glass Models (I) will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-557771