Giving the critical exponents explicitly in the equation of state, Arrott and Noakes proposed:
Where  are free parameters. In these modified Arrott plots, data is plotted as  versus . In the case of classical Landau theory,  and  and this equation reduces to the linear  versus  plot. However, the equation also allows for other values of  and , since real ferromagnets often do not have critical exponents exactly consistent with a simple mean field theory ferromagnetism.
The use of the correct critical exponents for a given system can help give straight lines on the Arott plot, but not in cases such as low magnetic field and amorphous materials. While mean field theory is a more reasonable model for ferromagnets at higher magnetic fields, the presence of more than one magnetic domain in real magnets means that especially at low magnetic fields, the experimentally measured macroscopic magnetic field (which is an average over the whole sample) will not be a reasonable way to determine the local magnetic field (which is felt by a single atom). Therefore, magnetization data taken at low magnetic fields should be ignored for the purposes of Arrott plots.