  We study the dynamics of the multipartite systems nonresonantly interacting
with electromagnetic fields and show that, since the coupling strength $g$ is
collectively enhanced by the square root of the number of microparticles
involved, the more rigorous large detuning condition for neglecting the rapidly
oscillating terms for the effective Hamiltonian should be $\Delta\gg\sqrt{N}g$,
instead of $\Delta\gg g$ usually used in the literature even in the case of
multipartite systems, with $\Delta$ the detuning and and $N$ the number of
microparticles. This result is significant since merely the satisfaction of the
original condition will result in the invalidity of the effective Hamiltonian
and the errors of the parameters associated with the detuning in the
multipartite case.
