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PreprintCC BY 4.0arXiv

The Blume-Capel Model as a ϕ6 Field Theory: A Monte Carlo and Flow Model Study

  • Ejaaz Merali
  • Ryan Larson
  • Ehsan Khatami
  • Richard T. Scalettar
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Abstract

We report Monte Carlo simulations of a continuous spin variant of the Blume-Capel model. We compute the phase diagrams in the crystal-field-temperature plane, as a function of the softness of the spins. We show that normalizing flows, a class of generative models capable of direct sampling without autocorrelation, are effective samplers across the phase diagram, including in the first-order transition region and in the vicinity of the tricritical point. Finite-size scaling analyses of flow samples locate the first- and second-order transitions as well as the tricritical point with accuracy comparable to canonical and extended-ensemble Monte Carlo.

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Cite

BibTeXRIS
BibTeX
@misc{merali2026blumecapel,
  title = {{The Blume-Capel Model as a $ϕ^6$ Field Theory: A Monte Carlo and Flow Model Study}},
  author = {Ejaaz Merali and Ryan Larson and Ehsan Khatami and Richard T. Scalettar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20982},
  eprint = {2610.20982},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20982},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Blume-Capel Model as a ϕ^6 Field Theory: A Monte Carlo and Flow Model Study
AU  - Ejaaz Merali
AU  - Ryan Larson
AU  - Ehsan Khatami
AU  - Richard T. Scalettar
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20982
UR  - https://arxiv.org/abs/2610.20982
AB  - We report Monte Carlo simulations of a continuous spin variant of the Blume-Capel model. We compute the phase diagrams in the crystal-field-temperature plane, as a function of the softness of the spins. We show that normalizing flows, a class of generative models capable of direct sampling without autocorrelation, are effective samplers across the phase diagram, including in the first-order transition region and in the vicinity of the tricritical point. Finite-size scaling analyses of flow samples locate the first- and second-order transitions as well as the tricritical point with accuracy comparable to canonical and extended-ensemble Monte Carlo.
ER  -