Let . The Curie-Weiss Model of ferromagnetism is the probability distribution defined as follows. For , define random variables with values in such that the probabilities are given by
where is the normalisation constant
(a) Show that for any .
(b) Show that . [You may use for all without proof. ]
(c) Let . Show that takes values in , and that for each the number of possible values of such that is
Find for any .