A surrogate by exchangeability approach to the Curie-Weiss model

We introduce a new general concept of surrogate random variable, the "surrogate by exchangeability" that allows to study the class of random variables that can be decomposed by means of an independent randomisation. As an example, we treat the case of the Curie-Weiss model using the 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, the surrogate study shows that the appearance 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.