Skip to content
DraconiticResearch
Search Sources API
194,230 studies31 sourcesUpdated 58 min ago
PreprintarXiv licencearXiv

New topological phase transitions in κ-deformed ϕ4 lattice models

  • Adith A
  • A. Bhagwat
Open at sourcePDFDOICite

Abstract

This paper explores topological phase transitions in the momentum space of the κ-deformed ϕ4 lattice model within the mean-field approximation. We show that the double-well structure of the momentum space gives rise to degenerate momentum states at high energies and that this change is marked by a phase transition. We investigate this transition using both numerical and analytical methods, with the analytical approach based primarily on singularity theory. Our numerical analysis shows that the energy at which the topological phase transition occurs is related to the noncommutative parameter by the simple power law E ∼ 1/α4. By mapping the constant-energy-level surface to the A3 singularity, we obtain the same result analytically. We also present results unique to noncommutative systems, showing that the fraction of particles in degenerate momentum states has a nonzero commutative limit. As a nonperturbative effect, this result provides a testable prediction for the existence of noncommutative spacetime.

Related

  1. Logarithmic transport at topological phase transitions of one-dimensional chiral quantum systems
    Dragan Markovic, Hermann Schulz-Baldes
    arXivPreprintarXiv licenceFull textMathematical physicsCondensed matterarXiv
  2. On exact solutions to three-dimensional Yukawa lattice model and BCC to FCC phase transitions
    Senping Luo, Juncheng Wei
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. Exact Scaling Laws and Non-Hermitian Topological Phase Transitions of Active Continuum on Hyperbolic Manifolds
    Yu-Xin Xie
    arXivPreprintCC0Full textMathematical physicsCondensed matterarXiv
  4. Lattice paths on snake graphs for q-deformed rationals
    Jérôme Germoni
    HALPreprintCC BY-NC-ND 4.0Full textCombinatorics & discrete mathematicsHALarXiv
  5. Quantum oscillations of helical edge states of periodically deformed 2D topological insulator in magnetic field
    A. V. Tsvetkova, P. D. Grigoriev, Ya. I. Rodionov
    arXivPreprintCC BY 4.0Full textMathematical physicsCondensed matterarXiv

Cite

BibTeXRIS
BibTeX
@misc{adith2026topological,
  title = {{New topological phase transitions in $κ$-deformed $ϕ^4$ lattice models}},
  author = {Adith A and A. Bhagwat},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15644},
  eprint = {2610.15644},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15644},
}
RIS
TY  - UNPB
TI  - New topological phase transitions in κ-deformed ϕ^4 lattice models
AU  - Adith A
AU  - A. Bhagwat
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15644
UR  - https://arxiv.org/abs/2610.15644
AB  - This paper explores topological phase transitions in the momentum space of the κ-deformed ϕ^4 lattice model within the mean-field approximation. We show that the double-well structure of the momentum space gives rise to degenerate momentum states at high energies and that this change is marked by a phase transition. We investigate this transition using both numerical and analytical methods, with the analytical approach based primarily on singularity theory. Our numerical analysis shows that the energy at which the topological phase transition occurs is related to the noncommutative parameter by the simple power law E ∼ 1/α^4. By mapping the constant-energy-level surface to the A_3 singularity, we obtain the same result analytically. We also present results unique to noncommutative systems, showing that the fraction of particles in degenerate momentum states has a nonzero commutative limit. As a nonperturbative effect, this result provides a testable prediction for the existence of noncommutative spacetime.
ER  -