Continuous Versus First Order Transitions in Compressible Diluted Magnets

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 dilutiondependent tricritical point beyond which, at stronger compressibility the transition is first order. The different behavior of XY and Heisenberg magnets is discussed. ∗Laboratoire associé au C.N.R.S. (U.A. n◦ 17) et aux Université Paris VII et Paris VI. 1