  We find the exact critical temperature $T_c$ of the nearest-neighbor
ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary
degree distribution $P(k)$. We observe an anomalous behavior of the
magnetization, magnetic susceptibility and specific heat, when $P(k)$ is
fat-tailed, or, loosely speaking, when the fourth moment of the distribution
diverges in infinite networks. When the second moment becomes divergent, $T_c$
approaches infinity, the phase transition is of infinite order, and size effect
is anomalously strong.
