  The scaling behavior of the order parameter at the chiral phase transition,
the so-called magnetic equation of state, of strongly interacting matter is
studied within effective models. We explore universal and nonuniversal
structures near the critical point. These include the scaling functions, the
leading corrections to scaling, and the corresponding size of the scaling
window as well as their dependence on an external symmetry breaking field. We
consider two models in the mean-field approximation, the quark-meson and the
Polyakov loop extended quark-meson (PQM) models, and compare their critical
properties with a purely bosonic theory, the $O(N)$ linear sigma model in the
$N\rightarrow \infty$ limit. In these models the order parameter scaling
function is found analytically using the high temperature expansion of the
thermodynamic potential. The effects of a gluonic background on the
nonuniversal scaling parameters are studied within the PQM model.
