Classical and quantum energies for interacting magnetic systems

The purpose of this paper 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.