  We study the thermodynamic behavior of branched polymers. We first study
random walks in order to clarify the thermodynamic relation between the
canonical ensemble and the grand canonical ensemble. We then show that
correlation functions for branched polymers are given by those for $\phi^3$
theory with a single mass insertion, not those for the $\phi^3$ theory
themselves. In particular, the two-point function behaves as $1/p^4$, not as
$1/p^2$, in the scaling region. This behavior is consistent with the fact that
the Hausdorff dimension of the branched polymer is four.
