  We investigate the Curie-Weiss model by means of an explicit construction of
its de Finetti measure of exchangeability. Writing the magnetisation as a sum
of i.i.d.'s randomised by the underlying De Finetti random variable, we show
that the apparition of a phase transition can be understood as a competition
between these two sources of randomness, the Gaussian regime corresponding to a
marginally relevant disordered system. The study is performed by introducing a
surrogate random variable that contains all the appropriate information on the
model and which is simpler to study.
