  We develop a theory for a generic instability of a Fermi liquid in dimension
d>1 against the formation of a Luttinger-liquid-like state. The density of
states at the Fermi level is the order parameter for the ensuing quantum phase
transition, which is driven by the effective interaction strength. A scaling
theory in conjunction with an effective field theoy for clean electrons is used
to obtain the critical behavior of observables. In the Fermi-liquid phase the
order-parameter susceptibility, which is measurable by tunneling, is predicted
to diverge for 1<d<3.
