Anisotropic scaling and generalized conformal invariance at Lifshitz points

Abstract

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.

4 pages, Latex, 2 figures

References in corpus (9)

• SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
• Scaling of magnetic fluctuations near a quantum phase transition
• Conformal Invariance for Non-Relativistic Field Theory
• Local scale invariance and strongly anisotropic equilibrium critical systems
• Critical behavior at m-axial Lifshitz points: field-theory analysis and $\epsilon$-expansion results
• Critical phenomena at perfect and non-perfect surfaces
• Exact Correlation Function at the Lifshitz Points of the Spherical Model
• Susceptibility Amplitude Ratios Near a Lifshitz Point
• Simulations on Infinite Size Lattices

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