  The interplay between disorder and compressibility in Ising magnets is
studied. Contrary to pure systems in which a weak compressibility drives the
transition first order, we find from a renormalization group analysis that it
has no effect on disordered systems which keep undergoing continuous transition
with rigid random-bond Ising model critical exponents. The mean field
calculation exhibits a dilution-dependent tricritical point beyond which, at
stronger compressibility the transition is first order. The different behavior
of XY and Heisenberg magnets is discussed.

Condensed Matter