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Critical amplitudes of the Baxter-Wu model from MCPA and Wolff simulations: free-exponent and fixed-exponent fits — arXiv:2611.04733

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.04733
License (as archived): CC0-1.0
Archived: 2026-11-04T13:03:28.130Z
SHA-256 of the archived text: 0c05a81cc64eb57e3316816ef7f8c334c8b3825a307d4f0e3d9cd1e14102d7c0
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How to cite

Critical amplitudes of the Baxter-Wu model from MCPA and Wolff simulations: free-exponent and fixed-exponent fits — arXiv:2611.04733 — arXiv (en), https://arxiv.org/abs/2611.04733 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_765dfd208a7b (Metraipolis archive dc_765dfd208a7b, sha256 0c05a81cc64eb57e3316816ef7f8c334c8b3825a307d4f0e3d9cd1e14102d7c0)

BibTeX

@misc{dc765dfd208a7b,
  title = {Critical amplitudes of the Baxter-Wu model from MCPA and Wolff simulations: free-exponent and fixed-exponent fits — arXiv:2611.04733},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.04733},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_765dfd208a7b; sha256 0c05a81cc64eb57e3316816ef7f8c334c8b3825a307d4f0e3d9cd1e14102d7c0},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.04733. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The two-dimensional Baxter-Wu model belongs to the universality class of the four-state Potts model. Exact expressions are available for its energy, specific heat, magnetization, and polarization amplitudes. We use these results as a benchmark for evaluating two simulation algorithms and two approaches to extracting critical amplitudes. Microcanonical population annealing (MCPA) and the sublattice-freezing Wolff algorithm yield highly consistent estimates for the energy and order parameters when applied to lattices of comparable size. According to the exact Joyce series, the local effective exponent does not stabilize at a constant value but instead undergoes a monotonic drift. This behaviour stems from corrections to scaling, which can be expressed as a series in the cube root of the reduced temperature. As a result, these corrections decay relatively slowly, with the leading term being of relative order $|t|^{2/3}$. When performing a fit with a free exponent on an automatically identified plateau, this drift gets incorporated into the estimated exponent, introducing a substantial bias in the derived amplitudes. In contrast, a fit that fixes the exponent to its exact value and explicitly accounts for the analytic correction series delivers a close match to the known exact amplitudes. Using this refined fitting approach, we obtain estimates for the susceptibility amplitudes and the universal amplitude ratios. These values are in good agreement with predictions from form-factor calculations. Additionally, we numerically determine the leading correction coefficient for the polarization.

Tema degli esploratori: fisica e astronomia (elenco arXiv cond-mat.stat-mech, nuovi lavori del giorno).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech).
Pagina del lavoro: https://arxiv.org/abs/2611.04733 — 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 2026-11-04T12:37:02.773Z dalla pagina https://arxiv.org/list/cond-mat.stat-mech/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).