  The Peierls instability in multi-channel metal nanowires is investigated.
Hyperscaling relations are established for the finite-size-, temperature-, and
wavevector-scaling of the electronic free energy. It is shown that the
softening of surface modes at wavevector $q=2k_{F,\nu}$ leads to critical
fluctuations of the wire's radius at zero temperature, where $k_{F,\nu}$ is the
Fermi wavevector of the highest occupied channel. This Peierls charge density
wave emerges as the system size becomes comparable to the channel correlation
length. Although the Peierls instability is weak in metal nanowires, in the
sense that the correlation length is exponentially long, we predict that
nanowires fabricated by current techniques can be driven into the
charge-density-wave regime under strain.
