  We employ non-perturbative flow equations to compute the equation of state
for two flavor QCD within an effective quark meson model. This yields the
temperature and quark mass dependence of quantities like the chiral condensate
or the pion mass. Our treatment covers both the chiral perturbation theory
domain of validity and the domain of validity of universality associated with
critical phenomena: We explicitly connect the physics at zero temperature and
realistic quark mass with the universal behavior near the critical temperature
$T_c$ and the chiral limit. For realistic quark masses the pion correlation
length near $T_c$ turns out to be smaller than its zero temperature value. In
the vicinity of $T_c$ and zero quark mass we obtain a precision estimate of the
universal critical equation of state. It belongs to the universality class of
the three dimensional O(4) symmetric Heisenberg model. We also investigate
scalar field theories directly in three dimensions near second order and first
order phase transitions. In particular, we obtain the universal equation of
state for weak first order phase transitions in scalar matrix models. We also
study the coarse grained free energy. Its dependence on the coarse graining
scale gives a quantitative criterion for the validity of Langer's theory of
spontaneous bubble nucleation.
