Lifshitz critical points meet Zamolodchikov perturbation theory
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≠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 ℳm,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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BibTeX
@article{antunes2026lifshitz,
title = {{Lifshitz critical points meet Zamolodchikov perturbation theory}},
author = {António Antunes},
journal = {Journal of High Energy Physics},
year = {2026},
month = jul,
doi = {10.1007/jhep07(2026)050},
eprint = {2602.12341},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05534778v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Lifshitz critical points meet Zamolodchikov perturbation theory
AU - António Antunes
PY - 2026
DA - 2026/07/03
JO - Journal of High Energy Physics
DO - 10.1007/jhep07(2026)050
UR - https://hal.science/hal-05534778v1
AB - 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 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.
SN - 1126-6708
SN - 1029-8479
ER -