Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2009-10-21
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 $0.915...\leq T \leq T_c=1$.
Crisanti Andrea
Dominicis Cirano de
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