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The quantum J1−J2 Blume–Capel model

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  • Guerrero, Alejandra I.

Abstract

In this study, it is investigated the effect of quantum fluctuations on the J1−J2 Blume–Capel model. The cluster mean field theory in the four site approximation is used to find the minimal (free) energy solutions. The ground state and finite temperature phase diagrams for the model with competitive ferromagnetic nearest neighbors (J1) and antiferromagnetic next nearest neighbors interactions (J2) are explored. It is found that the nature of phase transitions changes when quantum fluctuations and single-ion anisotropy parameter are varied. It is discussed the existence of tricritical points.

Suggested Citation

  • Guerrero, Alejandra I., 2025. "The quantum J1−J2 Blume–Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 658(C).
    • Handle: RePEc:eee:phsmap:v:658:y:2025:i:c:s0378437124008148
    DOI: 10.1016/j.physa.2024.130304
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    References listed on IDEAS

    as
    1. Schmidt, M. & Dias, P.F., 2021. "Correlated cluster mean-field theory for Ising-like spin systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    2. A. Kalz & A. Honecker & S. Fuchs & T. Pruschke, 2008. "Phase diagram of the Ising square lattice with competing interactions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(4), pages 533-537, October.
    3. Itacy José Souza & Mauricio Godoy & Alberto Sebastião de Arruda & Thiago Miranda Tunes, 2020. "Critical behavior of the spin-3/2 Blume-Capel quantum model with two random transverse single-ion anisotropies," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(12), pages 1-13, December.
    4. Muktish Acharyya & Bikas K. Chakrabarti, 2024. "Quantum Ising heat engines: a mean field study," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(4), pages 1-8, April.
    5. Benhouria, Y. & Essaoudi, I. & Ainane, A. & Ahuja, R. & Dujardin, F., 2018. "Hysteresis loops and dielectric properties of a mixed spin Blume–Capel Ising ferroelectric nanowire," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 499-506.
    6. Quentin Bouton & Jens Nettersheim & Sabrina Burgardt & Daniel Adam & Eric Lutz & Artur Widera, 2021. "A quantum heat engine driven by atomic collisions," Nature Communications, Nature, vol. 12(1), pages 1-7, December.
    7. Salgado, C.M. & de Carvalho, N.L. & de Arruda, P.H.Z. & Godoy, M. & de Arruda, A.S. & Costabile, Emanuel & de Sousa, J. Ricardo, 2019. "Random transverse single-ion anisotropy in the spin−1 Blume–Capel quantum model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 18-32.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Blume–Capel model; J1 – J2 transverse Ising model; Cluster mean field;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • J2 - Labor and Demographic Economics - - Demand and Supply of Labor

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