Anisotropic Scaling and Generalized Conformal Invariance at Lifshitz Points

The behaviour of the 3D axial next-nearest-neighbor Ising 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 $\alpha =0.18\mathrm{}\left(2\right)$, $\beta =0.238\mathrm{}\left(5\right)$, and $\gamma =1.36\mathrm{}\left(3\right)$. 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 at the Lifshitz point.