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PreprintCC BY 4.0HAL

Multiscale Loop Vertex Expansion for Cumulants, the ϕ42 Model

  • Vincent Rivasseau
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Abstract

We consider the ϕ42 model. It has been called the simplest non- trivial super-renormalisable model. The method we use is the multiscale loop vertex expansion, an improvement of constructive field theory. We prove analyticity and Borel summability of the cumulants up to a finite order.

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Cite

BibTeXRIS
BibTeX
@misc{rivasseau2026multiscale,
  title = {{Multiscale Loop Vertex Expansion for Cumulants, the $ϕ^4_2$ Model}},
  author = {Vincent Rivasseau},
  howpublished = {HAL},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.27188},
  eprint = {2608.27188},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05741420v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Multiscale Loop Vertex Expansion for Cumulants, the ϕ^4_2 Model
AU  - Vincent Rivasseau
PY  - 2026
DA  - 2026/08/31
PB  - HAL
DO  - 10.48550/arxiv.2608.27188
UR  - https://hal.science/hal-05741420v1
AB  - We consider the ϕ^4_2 model. It has been called the simplest non- trivial super-renormalisable model. The method we use is the multiscale loop vertex expansion, an improvement of constructive field theory. We prove analyticity and Borel summability of the cumulants up to a finite order.
ER  -