Anisotropic scaling and generalized conformal invariance at Lifshitz points

TL;DR

This study investigates the critical behavior of the 3D ANNNI model at the Lifshitz point using advanced Monte Carlo methods, revealing anisotropic scaling and conformal invariance generalizations.

Contribution

It introduces a new Monte Carlo approach and confirms the applicability of local scale invariance at the Lifshitz point.

Findings

Critical exponents: α=0.18(2), β=0.238(5), γ=1.36(3)

Correlation functions match the derived scaling function

Enhanced analysis of large systems with new algorithm

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.