Consider the correlation function \(g(r ; t, h)\) of Section 12.11 with \(h>0 .{ }^{22}\) Assume that this function has the following behavior:

\[
g(r) \sim e^{-r / \xi(t, h)} \times \text { some power of } r \quad(t \gtrsim 0) \text {, }
\]

such that \(\xi(0, h) \sim h^{-v^{c}}\). Show that \(v^{c}=v / \Delta\).

Next, assume that the susceptibility \(\chi(0, h) \sim h^{-\gamma^{c}}\). Show that \(\gamma^{c}=\gamma / \Delta=(\delta-1) / \delta\).