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PreprintarXiv licencearXiv

The long-range Ising CFT: perturbative and nonperturbative approaches

  • Zechuan Zheng
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Abstract

The long-range Ising model is the prototype of criticality with power-law interactions. In each dimension its interacting critical points form a one-parameter family of nonlocal conformal field theories, weakly coupled at both ends but not in between. We study this family in one, two and three dimensions from several independent directions. We extend the expansion about the generalized free field from three to eight loops and expand about the short-range end. We show that Hamiltonian truncation applies to this nonlocal theory once a truncation artifact is corrected. Where they can be compared, the resummed expansions, Hamiltonian truncation, the numerical renormalization group and Monte Carlo simulations agree on the dimension of the leading ℤ2-even scalar at the sub-percent level, as universality requires.

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Cite

BibTeXRIS
BibTeX
@misc{zheng2026longrange,
  title = {{The long-range Ising CFT: perturbative and nonperturbative approaches}},
  author = {Zechuan Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25940},
  eprint = {2610.25940},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25940},
}
RIS
TY  - UNPB
TI  - The long-range Ising CFT: perturbative and nonperturbative approaches
AU  - Zechuan Zheng
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.25940
UR  - https://arxiv.org/abs/2610.25940
AB  - The long-range Ising model is the prototype of criticality with power-law interactions. In each dimension its interacting critical points form a one-parameter family of nonlocal conformal field theories, weakly coupled at both ends but not in between. We study this family in one, two and three dimensions from several independent directions. We extend the expansion about the generalized free field from three to eight loops and expand about the short-range end. We show that Hamiltonian truncation applies to this nonlocal theory once a truncation artifact is corrected. Where they can be compared, the resummed expansions, Hamiltonian truncation, the numerical renormalization group and Monte Carlo simulations agree on the dimension of the leading ℤ_2-even scalar at the sub-percent level, as universality requires.
ER  -