  In [17], the authors have defined an annealed Ising model on random graphs
and proved limit theorems for the magnetization of this model on some random
graphs including random 2-regular graphs. Then in [11], we generalized their
results to the class of all random regular graphs. In this paper, we study the
critical behavior of this model. In particular, we determine the critical
exponents and prove a non standard limit theorem that the magnetization scaled
by n 3/4 converges to a specific random variable, with n the number of vertices
of random regular graphs.
