We present a detailed study of the phase diagram of the Ising model in random
graphs with arbitrary degree distribution. By using the replica method we
compute exactly the value of the critical temperature and the associated
critical exponents as a function of the minimum and maximum degree, and the
degree distribution characterizing the graph. As expected, there is a
ferromagnetic transition provided < \infty. However, if the fourth
moment of the degree distribution is not finite then non-trivial scaling
exponents are obtained. These results are analyzed for the particular case of
power-law distributed random graphs.Comment: 9 pages, 1 figur