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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 theexpansion is truncated to fourth order in. $Q_{ab} - Q^{({\rm RS})}_{ab}$. TheFull Replica Symmetry Broken (FRSB) solution is explicitly found but it turnsout to exist only in the range of temperature $0.549...\leq T\leq T_c=1$, notincluding 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 solutionthat exists in a limited temperature range $0.915...\leq T \leq T_c=1$.

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