  Based on a half-filled two-dimensional tight-binding model with
nearest-neighbour and next nearest-neighbour hopping the effect of imperfect
Fermi surface nesting on the Peierls instability is studied at zero
temperature. Two dimerization patterns corresponding to a phonon vector $(\pi,
\pi)$ are considered. It is found that the Peierls instability will be
suppressed with an increase of next nearest-neighbour hopping which
characterizes the nesting deviation. First and second order transitions to a
homogeneous state are possible. The competition between the two dimerized
states is discussed.
