  Among the Renormalization Group Theory scaling rules relating critical
exponents, there are hyperscaling rules involving the dimension of the system.
It is well known that in Ising models hyperscaling breaks down above the upper
critical dimension. It was shown by M. Schwartz [Europhys. Lett. {\bf 15}, 777
(1991)] that the standard Josephson hyperscaling rule can also break down in
Ising systems with quenched random interactions. A related Renormalization
Group Theory hyperscaling rule links the critical exponents for the normalized
Binder cumulant and the correlation length in the thermodynamic limit. An
appropriate scaling approach for analyzing measurements from criticality to
infinite temperature is first outlined. Numerical data on the scaling of the
normalized correlation length and the normalized Binder cumulant are shown for
the canonical Ising ferromagnet model in dimension three where hyperscaling
holds, for the Ising ferromagnet in dimension five (so above the upper critical
dimension) where hyperscaling breaks down, and then for Ising spin glass models
in dimension three where the quenched interactions are random. For the Ising
spin glasses there is a breakdown of the normalized Binder cumulant
hyperscaling relation in the thermodynamic limit regime, with a return to size
independent Binder cumulant values in the finite-size scaling regime around the
critical region.
