Field theory guides Monte Carlo in the one-dimensional long-range Ising model

Abstract

The statistical long-range Ising (LRI) model in one dimension provides a family of some of the simplest non-exactly solvable critical points. These critical points are described by long-range conformal field theories (CFTs) that are well understood analytically with perturbative expansions and some exact results. Guided by this, we revisit the Monte Carlo (MC) approach to the corresponding lattice model which has many favorable features compared to other systems studied with MC methods. In particular, with very modest computational cost, we are able to estimate scaling dimensions of leading and subleading operators as well as the associated three-point functions, and even certain four-point functions. These results help highlight the fact that 1d LRI CFTs are a phenomenal playground to more generally test non-perturbative methods and ideas for strongly coupled CFTs.

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BibTeX RIS

BibTeX

@misc{antunes2026field,
  title = {{Field theory guides Monte Carlo in the one-dimensional long-range Ising model}},
  author = {António Antunes and José Matos},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26838},
  eprint = {2610.26838},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26838},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Field theory guides Monte Carlo in the one-dimensional long-range Ising model
AU  - António Antunes
AU  - José Matos
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26838
UR  - https://arxiv.org/abs/2610.26838
AB  - The statistical long-range Ising (LRI) model in one dimension provides a family of some of the simplest non-exactly solvable critical points. These critical points are described by long-range conformal field theories (CFTs) that are well understood analytically with perturbative expansions and some exact results. Guided by this, we revisit the Monte Carlo (MC) approach to the corresponding lattice model which has many favorable features compared to other systems studied with MC methods. In particular, with very modest computational cost, we are able to estimate scaling dimensions of leading and subleading operators as well as the associated three-point functions, and even certain four-point functions. These results help highlight the fact that 1d LRI CFTs are a phenomenal playground to more generally test non-perturbative methods and ideas for strongly coupled CFTs.
ER  -

Abstract

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