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Phys Rev Lett. 2001 Sep 17;87(12):125702. Epub 2001 Aug 31.

Anisotropic scaling and generalized conformal invariance at Lifshitz points.

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Laboratoire de Physique des Matériaux, Université Henri Poincaré Nancy I, B.P. 239, F-54506 Vandoeuvre lès Nancy Cedex, France.


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(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 at the Lifshitz point.

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