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Detecting Multiple Phase Transitions in Lattice Systems with Intrinsic Dimensions — arXiv:2608.29090

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.29090
License (as archived): CC0-1.0
Archived: 2026-10-17T10:26:21.044Z
SHA-256 of the archived text: ded05a0e320e91168725c9263102e031302f6670295c2e805833b0aaf8c920b7
Stable URL of this page: https://metraipolis.com/documento/dc_7fbbea3fa4e9

How to cite

Detecting Multiple Phase Transitions in Lattice Systems with Intrinsic Dimensions — arXiv:2608.29090 — arXiv (en), https://arxiv.org/abs/2608.29090 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7fbbea3fa4e9 (Metraipolis archive dc_7fbbea3fa4e9, sha256 ded05a0e320e91168725c9263102e031302f6670295c2e805833b0aaf8c920b7)

BibTeX

@misc{dc7fbbea3fa4e9,
  title = {Detecting Multiple Phase Transitions in Lattice Systems with Intrinsic Dimensions — arXiv:2608.29090},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.29090},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7fbbea3fa4e9; sha256 ded05a0e320e91168725c9263102e031302f6670295c2e805833b0aaf8c920b7},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.29090. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Lattice systems with multiple nearby transitions pose two related challenges: resolving distinct transition scales and identifying the degrees of freedom primarily associated with each transition. We show that the intrinsic dimension of Monte Carlo configuration ensembles, estimated by the two-nearest-neighbors method, provides a geometric diagnostic for both problems. In the two-dimensional $q$-state clock model, the intrinsic dimension distinguishes the ordered, quasi-critical, and disordered regimes for both well-separated ($q=9$) and closely spaced ($q=5$) Berezinskii--Kosterlitz--Thouless transitions. In the $q=5$ case, the intermediate phase appears as a broad low-dimensional valley even when energy and magnetization do not separately resolve the two transitions. In the four-dimensional $U(1)$ Higgs model, we introduce channel-decomposed intrinsic dimensions based on gauge-invariant plaquette and Higgs variables. The dominant response of each channel tracks transitions associated with the corresponding degrees of freedom, while the combined channel retains features of both. We further show that intrinsic dimensions evaluated directly on gauge-variant fields are dominated by gauge-orbit directions, demonstrating the importance of removing gauge redundancy before interpreting configuration-space geometry. These results establish channel-decomposed intrinsic dimension as a geometric probe of lattice systems with multiple transitions and motivate its application to disentangling deconfinement and chiral crossover scales in full QCD.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-01 in physics.data-an).
Categorie arXiv: High Energy Physics - Lattice (hep-lat) ; Data Analysis, Statistics and Probability (physics.data-an).
Pagina del lavoro: https://arxiv.org/abs/2608.29090 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T10:13:57.280Z dalla pagina https://arxiv.org/catchup/physics.data-an/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).