Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-04-06
J. Phys. A 37, 7433-7446 (2004)
Physics
Condensed Matter
Disordered Systems and Neural Networks
19 pages, revtex4
Scientific paper
10.1088/0305-4470/37/30/003
We study a finite range spin glass model in arbitrary dimension, where the intensity of the coupling between spins decays to zero over some distance $\gamma^{-1}$. We prove that, under a positivity condition for the interaction potential, the infinite-volume free energy of the system converges to that of the Sherrington-Kirkpatrick model, in the Kac limit $\gamma\to0$. We study the implication of this convergence for the local order parameter, i.e., the local overlap distribution function and a family of susceptibilities to it associated, and we show that locally the system behaves like its mean field analogue. Similar results are obtained for models with $p$-spin interactions. Finally, we discuss a possible approach to the problem of the existence of long range order for finite $\gamma$, based on a large deviation functional for overlap profiles. This will be developed in future work.
Franz Silvio
Toninelli Fabio Lucio
No associations
LandOfFree
Finite-range spin glasses in the Kac limit: free energy and local observables 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 Finite-range spin glasses in the Kac limit: free energy and local observables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite-range spin glasses in the Kac limit: free energy and local observables will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-600782