  The purpose of this article is to give different interpretations of the first
non vanishing term (quadratic) of the ground state asymptotic expansion for a
spin system in quantum electrodynamics, as the spin magnetic moments go to $0$.
One of the interpretations makes a direct link with some classical physics
laws. A central role is played by an operator $A_M$ acting only in the finite
dimensional spin state space and making the connections with the different
interpretations, and also being in close relation with the multiplicity of the
ground state.
