The Thermodynamic Limit in Mean Field Spin Glass Models

Details The Thermodynamic Limit in Mean Field Spin Glass Models The Thermodynamic Limit in Mean Field Spin Glass Models

2002-04-12

arxiv.org/abs/cond-mat/0204280v1

Commun. Math. Phys. 230 (2002) 1, 71-79

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages

Scientific paper

10.1007/s00220-002-0699-y

We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and the Derrida p-spin model. The main argument is based on a smooth interpolation between a large system, made of N spin sites, and two similar but independent subsystems, made of N_1 and N_2 sites, respectively, with N_1+N_2=N. The quenched average of the free energy turns out to be subadditive with respect to the size of the system. This gives immediately convergence of the free energy per site, in the infinite volume limit. Moreover, a simple argument, based on concentration of measure, gives the almost sure convergence, with respect to the external noise. Similar results hold also for the ground state energy per site.

Affiliated with

Also associated with

No associations

Rating

The Thermodynamic Limit in Mean Field Spin Glass Models 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 The Thermodynamic Limit in Mean Field Spin Glass Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Thermodynamic Limit in Mean Field Spin Glass Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-667390