Lifshitz critical points meet Zamolodchikov perturbation theory

António Antunes

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arXiv · 2602.12341

Lifshitz critical points meet Zamolodchikov perturbation theory

António Antunes

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Abstract

Critical points of classical and quantum lattice models are often described by scale-invariant Lifshitz theories which are anisotropic in the continuum limit, as characterized by a dynamical critical exponent $z\neq1$. This type of critical behavior can in principle be studied by deforming ordinary $z=1$ conformal field theories (CFTs) by relevant vector operators breaking the rotational/Lorentz symmetry. In this short note, we consider a two-dimensional system of coupled minimal model CFTs $\mathcal{M}_{m,m+1}$ which realizes this perspective in a controlled fashion via Zamolodchikov's large $m$ expansion. The model turns out to exhibit interesting properties, including a manifold of interacting Lifshitz fixed points and emergent rotational symmetry in the infrared.

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António Antunes. 2026-02-12. Lifshitz critical points meet Zamolodchikov perturbation theory. https://arxiv.org/abs/2602.12341

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