  We discuss chiral symmetry breaking critical points from the perspective of
PCAC, correlation length scaling and the chiral equation of state. A scaling
theory for the ratio $R_\pi$ of the pion to sigma masses is presented. The
Goldstone character of the pion and properties of the longitudinal and
transverse chiral susceptibilities determine the ratio $R_\pi$ which can be
used to locate critical points and measure critical indices such as $\delta$.
We show how PCAC and correlation length scaling determine the pion mass'
dependence on the chiral condensate and lead to a practical method to measure
the anomalous dimension $\eta$. These tools are proving useful in studies of
the chiral transition in lattice QED and the quark-gluon plasma transition in
lattice QCD.
