Arrott plot ($M^2=({\mu }_0/b)(H/M)-a/b$)

An Arrott plot presents squared magnetisation against field divided by magnetisation. For the uniform SI Landau equation ${\mu }_{0}H=aM+b{M}^3$, it is a straight lineThe critical mean-field isotherm has $a=0$ and passes through the origin. Horizontal intercept $a/{\mu }_0$ changes sign across the transition; a positive vertical intercept estimates spontaneous magnetisation squared. The original criterion concerns internal magnetic field and the molecular-field regime. Demagnetizing fields and non-mean-field critical exponents require additional care.^[ref]

If physical ordinate is $Y=M^2$ and abscissa $X=H/M$, slope $S=dY/dX$ and horizontal intercept $X_0$ give $b={\mu }_0/S$ and $a={\mu }_0{X}_0$. Any displayed squared-magnetisation scale must be converted before using S. For example, an ordinate unit $(10^4\mathrm{A}{\mathrm{m}}^{-1}{)}^2$ equals $10^8{\mathrm{A}}^2{\mathrm{m}}^{-2}$, not $10^4$. With a free-energy density, the resulting units are $[a]=\mathrm{H}{\mathrm{m}}^{-1}$ and $[b]=\mathrm{J}\mathrm{m}{\mathrm{A}}^{-4}$. Curvature or differing isotherm slopes limits the accuracy of a constant-coefficient fit.