  We study the quark mass dependence of various response functions, which
contribute to chiral susceptibilities and the specific heat in the staggered
fermion formulation of two-flavour QCD. This yields information about the
critical exponents $\alpha$, $\beta$ and $\delta$. In the case of the chiral
susceptibility, obtained as derivative of the chiral order parameter with
respect to the quark mass, we calculate all contributions. This allows to
construct a cumulant of the order parameter, which is a scaling function and
yields a direct determination of the critical exponent $\delta$. All our
results are consistent with a second order phase transition.
