Sherrington-Kirkpatrick model near $T=T_c$: expanding around the Replica Symmetric Solution

Details Sherrington-Kirkpatrick model near $T=T_c$: expanding around the Replica Symmetric Solution Sherrington-Kirkpatrick model near $T=T_c$: expanding around the Replica Symmetric Solution

2009-10-21

arxiv.org/abs/0910.4091v2

J. Phys. A: Math. Theor. 43 (2010) 055002

Physics

Condensed Matter

Disordered Systems and Neural Networks

18 pages, 3 figures

Scientific paper

10.1088/1751-8113/43/5/055002

An expansion for the free energy functional of the Sherrington-Kirkpatrick (SK) model, around the Replica Symmetric SK solution $Q^{({\rm RS})}_{ab} = \delta_{ab} + q(1-\delta_{ab})$ is investigated. In particular, when the expansion is truncated to fourth order in. $Q_{ab} - Q^{({\rm RS})}_{ab}$. The Full Replica Symmetry Broken (FRSB) solution is explicitly found but it turns out to exist only in the range of temperature $0.549...\leq T\leq T_c=1$, not including T=0. On the other hand an expansion around the paramagnetic solution $Q^{({\rm PM})}_{ab} = \delta_{ab}$ up to fourth order yields a FRSB solution that exists in a limited temperature range $0.915...\leq T \leq T_c=1$.

Affiliated with

Also associated with

No associations

Rating

Sherrington-Kirkpatrick model near $T=T_c$: expanding around the Replica Symmetric Solution 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 Sherrington-Kirkpatrick model near $T=T_c$: expanding around the Replica Symmetric Solution, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sherrington-Kirkpatrick model near $T=T_c$: expanding around the Replica Symmetric Solution will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-144289