  We consider a $\phi^4$-theory with a position-dependent distance from the
critical point. One realization of this model is a classical ferromagnet
subject to non-uniform mechanical stress. We find a sharp phase transition
where the envelope of the local magnetization vanishes uniformly. The
first-order transition in a quantum ferromagnet also remains sharp. The
universal mechanism leading to a tricritical point in an itinerant quantum
ferromagnet is suppressed, and in principle one can recover a quantum critical
point with mean-field exponents. Observable consequences of these results are
discussed.
