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PreprintCC BY 4.0arXiv

A Finite-Range, Translation-Invariant Counterexample to Weak Gibbsianity

  • Lorenzo Pettinari
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Abstract

We construct a finite-range, translation-invariant counterexample to the Weak Gibbsianity property for quantum spin systems on ℤ2. The proof relies on showing how a local potential can induce macroscopically large deviations from an equilibrium configuration after a perturbation is introduced at the boundary of the lattice.

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Cite

BibTeXRIS
BibTeX
@misc{pettinari2026finiterange,
  title = {{A Finite-Range, Translation-Invariant Counterexample to Weak Gibbsianity}},
  author = {Lorenzo Pettinari},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41871},
  eprint = {2610.41871},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41871},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Finite-Range, Translation-Invariant Counterexample to Weak Gibbsianity
AU  - Lorenzo Pettinari
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41871
UR  - https://arxiv.org/abs/2610.41871
AB  - We construct a finite-range, translation-invariant counterexample to the Weak Gibbsianity property for quantum spin systems on ℤ^2. The proof relies on showing how a local potential can induce macroscopically large deviations from an equilibrium configuration after a perturbation is introduced at the boundary of the lattice.
ER  -