  We investigate nanoelectromechanical systems near mechanical instabilities.
We show that quite generally, the interaction between the electronic and the
vibronic degrees of freedom can be accounted for essentially exactly when the
instability is continuous. We apply our general framework to the Euler buckling
instability and find that the interaction between electronic and vibronic
degrees of freedom qualitatively affects the mechanical instability, turning it
into a discontinuous one in close analogy with tricritical points in the Landau
theory of phase transitions.
