  The critical properties of systems under constraint differ from their ideal
counterparts through Fisher renormalization. The mathematical properties of
Fisher renormalization applied to critical exponents are well known: the
renormalized indices obey the same scaling relations as the ideal ones and the
transformations are involutions in the sense that re-renormalizing the critical
exponents of the constrained system delivers their original, ideal
counterparts. Here we examine Fisher renormalization of critical amplitudes and
show that, unlike for critical exponents, the associated transformations are
not involutions. However, for ratios and combinations of amplitudes which are
universal, Fisher renormalization is involutory.
