  We introduce varying spin strengths to the Ising model, a central pillar of
statistical physics. With inhomogeneous physical systems in mind, but also
anticipating interdisciplinary applications, we present the model on network
structures of varying degrees of complexity. We solve it for the generic case
of power-law spin strength and find that, with a self-averaging free energy,
the model has a rich phase diagram with new universality classes. Indeed, the
degree of complexity added by variable spins is on a par to that added by
endowing simple networks with increasingly realistic geometries. It is suitable
for modeling emergent phenomena in many-body systems in contexts where
non-identicality of spins or agents plays an essential role and for exporting
statistical physics concepts beyond physics.
