  The behaviour of the 3D axial next-nearest neighbour Ising (ANNNI) model at
the uniaxial Lifshitz point is studied using Monte Carlo techniques. A new
variant of the Wolff cluster algorithm permits the analysis of systems far
larger than in previous studies. The Lifshitz point critical exponents are
$\alpha=0.18(2)$, $\beta=0.238(5)$ and $\gamma=1.36(3)$. Data for the spin-spin
correlation function are shown to be consistent with the explicit scaling
function derived from the assumption of local scale invariance, which is a
generalization of conformal invariance to the anisotropic scaling {\em at} the
Lifshitz point.
