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<p>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 <i>z</i> ≠ 1. This type of critical behavior can in principle be studied by deforming ordinary <i>z</i> = 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 <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">M</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {\mathcal{M}}_{m,m+1} \)</EquationSource> </InlineEquation> which realizes this perspective in a controlled fashion via Zamolodchikov’s large <i>m</i> expansion. The model turns out to exhibit interesting properties, including a manifold of interacting Lifshitz fixed points and emergent rotational symmetry in the infrared.</p>

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Lifshitz critical points meet Zamolodchikov perturbation theory

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月3日

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  • António Antunes

摘要

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 ≠ 1. 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 M m , m + 1 \( {\mathcal{M}}_{m,m+1} \) 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.