Exponent inference from a magnetic data collapse ($\alpha =2-2\beta -\gamma ,\nu =(2\beta +\gamma )/d$)

If magnetic data collapse with independently specified critical exponents $\beta ,\gamma$, the ordinary scaling identities infer $\Delta =\beta +\gamma$, $\delta =1+\gamma /\beta$, and the displayed exponents. The Fisher scaling relation then gives $\eta =2-\gamma /\nu$. These are conditional inferences, not five additional independent measurements. Hyperscaling is needed for the spatial exponents, and subtraction can make small inferred $\alpha$ or $\eta$ unusually sensitive to uncertainty. A slope on linear axes is not a fitted logarithmic exponent.