  The energy of a type II superconductor submitted to an external magnetic
field of intensity close to the second critical field is given by the
celebrated Abrikosov energy. If the external magnetic field is comparable to
and below the second critical field, the energy is given by a reference
function obtained as a special (thermodynamic) limit of a non-linear energy. In
this note, we give a new formula for this reference energy. In particular, we
obtain it as a special limit of a {\it linear} energy defined over
configurations normalized in the $L^4$-norm.
