Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Seeded bubble nucleation on the lattice

Simone Blasi1,*, Andreas Ekstedt2, Jaakko Hällfors3,†, and Kari Rummukainen3,‡

  • *Contact author: simone.blasi@desy.de
  • †Contact author: jaakko.hallfors@helsinki.fi
  • ‡Contact author: kari.rummukainen@helsinki.fi

Phys. Rev. D 114, 074505 – Published 6 October, 2026

DOI: https://doi.org/10.1103/nyt6-jh16

Abstract

We provide the first nonperturbative lattice determination of the bubble nucleation rate as seeded by topological defects during a first-order phase transition. Our case of study is the cubic anisotropy model, which can mimic the Higgs-plus-singlet setup for the electroweak theory, in d=2+1 spacetime dimensions, where bubbles are seeded by (linelike) domain walls. We compare the nucleation rate from the lattice with the semiclassical prediction based on the effective field theory living on the domain walls, including for the first time the fluctuation determinant away from spherical symmetry. Our results show very good agreement across all the considered parameter space.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (55)

  1. A. D. Linde, Phys. Lett. 100B, 37 (1981).
  2. A. D. Linde, Nucl. Phys. B216, 421 (1983); B223, 544(E) (1983).
  3. S. Blasi and A. Mariotti, Phys. Rev. Lett. 129, 261303 (2022).
  4. P. Agrawal, S. Blasi, A. Mariotti, and M. Nee, J. High Energy Phys. 06 (2023) 089.
  5. S. Blasi, R. Jinno, T. Konstandin, H. Rubira, and I. Stomberg, J. Cosmol. Astropart. Phys. 10 (2023) 051.
  6. Y. Bai, Y. Xu, and Y. Yang, J. Cosmol. Astropart. Phys. 05 (2026) 036.
  7. P. J. Steinhardt, Phys. Rev. D 24, 842 (1981).
  8. P. J. Steinhardt, Nucl. Phys. B190, 583 (1981).
  9. U. A. Yajnik, Phys. Rev. D 34, 1237 (1986).
  10. U. A. Yajnik and T. Padmanabhan, Phys. Rev. D 35, 3100 (1987).
  11. I. Dasgupta, Nucl. Phys. B506, 421 (1997).
  12. B.-H. Lee, W. Lee, R. MacKenzie, M. B. Paranjape, U. A. Yajnik, and D.-h. Yeom, Phys. Rev. D 88, 105008 (2013).
  13. S. Blasi and A. Mariotti, SciPost Phys. 18, 016 (2025).
  14. A. Chatrchyan, F. Niedermann, and P. Richman-Taylor, Phys. Rev. D 113, 043535 (2026).
  15. B. Kumar and U. Yajnik, Nucl. Phys. B831, 162 (2010).
  16. B. Kumar, M. B. Paranjape, and U. A. Yajnik, Phys. Rev. D 82, 025022 (2010).
  17. P. Agrawal and M. Nee, SciPost Phys. 13, 049 (2022).
  18. C. Caprini et al., J. Cosmol. Astropart. Phys. 03 (2019) 024.
  19. E. Witten, Phys. Rev. D 30, 272 (1984).
  20. S. R. Coleman, Phys. Rev. D 15, 2929 (1977); 16, 1248(E) (1977).
  21. C. G. Callan, Jr. and S. R. Coleman, Phys. Rev. D 16, 1762 (1977).
  22. J. S. Langer, Ann. Phys. (N.Y.) 54, 258 (1969).
  23. G. D. Moore, K. Rummukainen, and A. Tranberg, J. High Energy Phys. 04 (2001) 017.
  24. G. D. Moore and K. Rummukainen, Phys. Rev. D 63, 045002 (2001).
  25. O. Gould, S. Güyer, and K. Rummukainen, Phys. Rev. D 106, 114507 (2022); 110, 119903(E) (2024).
  26. O. Gould, A. Kormu, and D. J. Weir, Phys. Rev. D 111, L051901 (2025).
  27. L. Niemi, M. J. Ramsey-Musolf, and G. Xia, Phys. Rev. D 110, 115016 (2024).
  28. A. Horowitz, Phys. Lett. 156B, 89 (1985).
  29. S. Ryang, T. Saito, and K. Shigemoto, Prog. Theor. Phys. 73, 1295 (1985).
  30. D. Bodeker, Nucl. Phys. B486, 500 (1997).
  31. G. Aarts and J. Smit, Nucl. Phys. B511, 451 (1998).
  32. D. Grigoriev and V. Rubakov, Nucl. Phys. B299, 67 (1988).
  33. A. Bochkarev and P. De Forcrand, Phys. Rev. Lett. 63, 2337 (1989).
  34. M. Alford, H. Feldman, and M. Gleiser, Phys. Rev. Lett. 68, 1645 (1992).
  35. O. T. Valls and G. F. Mazenko, Phys. Rev. B 42, 6614 (1990).
  36. M. Alford and M. Gleiser, Phys. Rev. D 48, 2838 (1993).
  37. S. Borsanyi, A. Patkos, J. Polonyi, and Z. Szep, Phys. Rev. D 62, 085013 (2000).
  38. D. Pîrvu, A. Shkerin, and S. Sibiryakov, Int. J. Mod. Phys. A 39, 2445007 (2024).
  39. L. Batini, A. Chatrchyan, and J. Berges, Phys. Rev. D 109, 023502 (2024).
  40. J. Hirvonen and O. Gould, Phys. Rev. Lett. 136, 081601 (2026).
  41. D. Pîrvu, A. Shkerin, and S. Sibiryakov, arXiv:2407.06263.
  42. A. Ekstedt, O. Gould, and J. Hirvonen, J. High Energy Phys. 12 (2023) 056.
  43. J. S. Langer, Ann. Phys. (N.Y.) 41, 108 (1967).
  44. J. S. Langer, Ann. Phys. (N.Y.) 54, 258 (1969).
  45. L. P. Csernai and J. I. Kapusta, Phys. Rev. D 46, 1379 (1992).
  46. A. Berera, J. Mabillard, B. W. Mintz, and R. O. Ramos, Phys. Rev. D 100, 076005 (2019).
  47. O. Gould and J. Hirvonen, Phys. Rev. D 104, 096015 (2021).
  48. A. Ekstedt, J. High Energy Phys. 08 (2022) 115.
  49. J. Hirvonen, Phys. Rev. D 111, 116020 (2025).
  50. G. V. Dunne, J. Phys. A 41, 304006 (2008).
  51. HILA lattice simulation framework, https://github.com/CFT-HY/HILA.
  52. H. Yoshida, Phys. Lett. A 150, 262 (1990).
  53. B. Leimkuhler and C. Matthews, Molecular Dynamics: With Deterministic and Stochastic Numerical Methods (Springer, New York, 2015), Vol. 39.
  54. C. L. Wainwright, Comput. Phys. Commun. 183, 2006 (2012).
  55. K. Rummukainen, S. Blasi, J. Hällfors, and A. Ekstedt, Zenodo Version v1. (2026).10.5281/zenodo.22743061.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation