  We study the critical behavior of the ferromagnetic Ising model on random
trees as well as so-called locally tree-like random graphs. We pay special
attention to trees and graphs with a power-law offspring or degree distribution
whose tail behavior is characterized by its power-law exponent $\tau>2$. We
show that the critical temperature of the Ising model equals the inverse
hyperbolic tangent of the inverse of the mean offspring or mean forward degree
distribution. In particular, the inverse critical temperature equals zero when
$\tau\in(2,3]$ where this mean equals infinity.
  We further study the critical exponents $\delta, \beta$ and $\gamma$,
describing how the (root) magnetization behaves close to criticality. We
rigorously identify these critical exponents and show that they take the values
as predicted by Dorogovstev, et al. and Leone et al. These values depend on the
power-law exponent $\tau$, taking the mean-field values for $\tau>5$, but
different values for $\tau\in(3,5)$.
