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Unconventional criticality in O(D)-invariant loop-constrained Landau theory

Svitlana Kondovych1,*, Asle Sudbø2, and Flavio S. Nogueira1

  • *Contact author: s.kondovych@ifw-dresden.de
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Phys. Rev. Research 8, 013186 – Published 19 February, 2026

DOI: https://doi.org/10.1103/mq1b-z531

Abstract

We study an unconventional phase transition in ferroelectrics where the polarization field is constrained to be divergence-free, allowing only looplike configurations. This local constraint fundamentally alters the critical behavior, driving the system beyond the Landau-Ginzburg-Wilson paradigm. A renormalization group analysis shows that the polarization acquires an unusually large anomalous dimension, η≈0.239 in three dimensions, far exceeding the typical values in O(3)-invariant systems. We attribute this effect to a naturally induced gauge symmetry originating from the zero-divergence constraint. Such constraint-induced gauge-field behavior is reminiscent of fractionalized phases, revealing a fundamental connection between constrained ferroelectrics and emergent gauge phenomena in correlated matter.

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References (42)

  1. T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. Fisher, Deconfined quantum critical points, Science 303, 1490 (2004).
  2. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2011).
  3. A. Prakash and N. G. Jones, Classical origins of Landau-incompatible transitions, Phys. Rev. Lett. 134, 097103 (2025).
  4. T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, and M. P. A. Fisher, Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm, Phys. Rev. B 70, 144407 (2004).
  5. C. L. Henley, The “Coulomb phase” in frustrated systems, Annu. Rev. Condens. Matter Phys. 1, 179 (2010).
  6. R. Moessner and S. L. Sondhi, Resonating valence bond phase in the triangular lattice quantum dimer model, Phys. Rev. Lett. 86, 1881 (2001).
  7. F. S. Nogueira and Z. Nussinov, Renormalization, duality, and phase transitions in two- and three-dimensional quantum dimer models, Phys. Rev. B 80, 104413 (2009).
  8. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Hoboken, NJ, 1998).
  9. J. P. Freidberg, Ideal MHD (Cambridge University Press, Cambridge, 2014).
  10. V. I. Arnold and B. A. Khesin, Topological Methods in Hydrodynamics (Springer Science & Business Media, New York, 2021), Vol. 125.
  11. I. Luk’yanchuk, Y. Tikhonov, A. Razumnaya, and V. M. Vinokur, Hopfions emerge in ferroelectrics, Nat. Commun. 11, 2433 (2020).
  12. S. Kondovych, M. Pavlenko, Y. Tikhonov, A. Razumnaya, and I. Lukyanchuk, Vortex states in a PbTiO3 ferroelectric cylinder, SciPost Phys. 14, 056 (2023).
  13. F. Di Rino, L. Boron, M. A. Pavlenko, I. A. Tikhonov, A. G. Razumnaya, M. Sepliarsky, A. Sené, I. A. Lukyanchuk, and S. Kondovych, Topological states in ferroelectric nanorods tuned by the surface tension, Commun. Mater. 6, 57 (2025).
  14. I. A. Lukyanchuk, A. G. Razumnaya, S. Kondovych, Y. A. Tikhonov, B. Khesin, and V. M. Vinokur, Topological foundations of ferroelectricity, Phys. Rep. 1110, 1 (2025).
  15. X. Guo, L. Zhou, B. Roul, Y. Wu, Y. Huang, S. Das, and Z. Hong, Theoretical understanding of polar topological phase transitions in functional oxide heterostructures: A review, Small Methods 6, 2200486 (2022).
  16. Y. Wang, Y. Tang, Y. Zhu, and X. Ma, Entangled polarizations in ferroelectrics: A focused review of polar topologies, Acta Mater. 243, 118485 (2023).
  17. I. Luk’yanchuk, A. Razumnaya, S. Kondovych, Y. Tikhonov, and V. M. Vinokur, Topological ferroelectric chirality, arXiv:2406.19728.
  18. R. P. Feynman, Application of quantum mechanics to liquid helium, in Progress in Low Temperature Physics, edited by C. J. Gorter (North-Holland Publishing Company, Amsterdam, 1955), Chap. II, Vol. 1, pp. 17–53.
  19. A. L. Fetter, Quantum theory of superfluid vortices. I. Liquid helium II, Phys. Rev. 162, 143 (1967).
  20. L. Onsager, Discussion at an international conference on statistical mechanics, Nuovo Cim. Suppl. 6, 249 (1949).
  21. S. R. Shenoy, Vortex-loop scaling in the three-dimensional XY ferromagnet, Phys. Rev. B 40, 5056 (1989).
  22. A. K. Nguyen and A. Sudbø, Onsager loop transition and first-order flux-line lattice melting in high-Tc superconductors, Phys. Rev. B 57, 3123 (1998).
  23. V. L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. Classical systems, Sov. Phys. JETP 32, 493 (1971).
  24. J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C: Solid State Phys. 6, 1181 (1973).
  25. H. Kleinert and V. Schulte-Frohlinde, Critical Properties of ϕ4-Theories (World Scientific, Singapore, 2001).
  26. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 5th ed. (Oxford University Press, Oxford, 2021), Vol. 171.
  27. P. Minnhagen, The two-dimensional Coulomb gas, vortex unbinding, and superfluid-superconducting films, Rev. Mod. Phys. 59, 1001 (1987).
  28. J. Fröhlich and T. Spencer, On the statistical mechanics of classical Coulomb and dipole gases, J. Stat. Phys. 24, 617 (1981).
  29. S. Kragset, A. Sudbø, and F. S. Nogueira, Metal-insulator transition in two- and three-dimensional logarithmic plasmas, Phys. Rev. Lett. 92, 186403 (2004).
  30. I. Efe, N. A. Spaldin, and C. Gattinoni, On the happiness of ferroelectric surfaces and its role in water dissociation: The example of bismuth ferrite, J. Chem. Phys. 154, 024702 (2021).
  31. R. D. Johnson, L. C. Chapon, D. D. Khalyavin, P. Manuel, P. G. Radaelli, and C. Martin, Giant improper ferroelectricity in the ferroaxial magnet CaMn7O12, Phys. Rev. Lett. 108, 067201 (2012).
  32. J. Hlinka, J. Privratska, P. Ondrejkovic, and V. Janovec, Symmetry guide to ferroaxial transitions, Phys. Rev. Lett. 116, 177602 (2016).
  33. T. Hayashida, Y. Uemura, K. Kimura, S. Matsuoka, D. Morikawa, S. Hirose, K. Tsuda, T. Hasegawa, and T. Kimura, Visualization of ferroaxial domains in an order-disorder type ferroaxial crystal, Nat. Commun. 11, 4582 (2020).
  34. B. Singh, et al., Ferroaxial density wave from intertwined charge and orbital order in rare-earth tritellurides, Nat. Phys. 21, 1578 (2025).
  35. L. D. Landau, E. Lifshitz, and L. Pitaevskii, Electrodynamics of Continuous Media (Elsevier, Oxford, 2013), Vol. 8.
  36. C. Itzykson and J.-M. Drouffe, Statistical Field Theory (Cambridge University Press, Cambridge, 1991), Vol. 1.
  37. M. E. Fisher and M. N. Barber, Scaling theory for finite-size effects in the critical region, Phys. Rev. Lett. 28, 1516 (1972).
  38. J. Koch and R. Sabirianov, Finite size effects in shell nanoparticles, J. Magn. Magn. Mater. 321, 1137 (2009).
  39. X. Pham Phu, V. Thanh Ngo, and H. Diep, Critical behavior of magnetic thin films, Surf. Sci. 603, 109 (2009).
  40. H. Baaziz, A. Tozri, E. Dhahri, and E. Hlil, Size reduction effect on the critical behavior near the paramagnetic to ferromagnetic phase transition temperature in La0.9Sr0.1MnO3 nanoparticles, Solid State Commun. 208, 45 (2015).
  41. J. C. Collins, Renormalization: An Introduction to Renormalization, the Renormalization Group and the Operator-Product Expansion (Cambridge University Press, Cambridge, 1984).
  42. A. Aharony, Critical behavior of magnets with dipolar interactions. V. Uniaxial magnets in d dimensions, Phys. Rev. B 8, 3363 (1973).

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Phys. Rev. Research 8, 013186– Published 19 February, 2026
  • Received 15 October 2025
  • Accepted 31 January 2026
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