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We examine the thermal pairwise entanglement in a symmetric system of $n$spins fully connected through anisotropic $XYZ$-type couplings embedded in atransverse magnetic field. We consider both the exact evaluation together withthat obtained with the static path + random phase approximation (RPA) and theensuing mean field + RPA. The latter is shown to provide an accurate analyticdescription of both the parallel and antiparallel thermal concurrence in largesystems. We also analyze the limit temperature for pairwise entanglement, whichis shown to increase for large fields and to decrease logarithmically withincreasing $n$. Special finite size effects are as well discussed.

Thermal entanglement in fully connected spin systems and its RPA description