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Studying the Effect of Strong Magnetic Fields on the Phase Transitions of the Frustrated Potts Model with a Number of Spin States q = 4

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Abstract

The phase transitions and thermodynamic properties of the two-dimensional Potts model with a number of spin states q = 4 are studied on the basis of a replica algorithm by the Monte Carlo method on a hexagonal lattice with consideration for the interaction between the first and second nearest neighbors in an external magnetic field. The studies are performed for magnetic field values within a range 0.0 ≤ h ≤ 7.0 with a step of 1.0. The magnetic structures of the ground states are constructed. It is revealed that a first-order phase transition occurs within the considered range of magnetic field values. It is demonstrated that magnetic field within a range 4.0 ≤ h ≤ 7.0 lifts the ground state degeneracy, and the phase transition becomes smeared.

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REFERENCES

  1. H. T. Diep, Frustrated Spin Systems (World Scientific, Singapore, 2004), p. 624.

    Google Scholar 

  2. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, New York, 1982; Mir, Moscow, 1985).

  3. F. Y. Wu, Exactly Solved Models. A Journey in Statistical Mechanics (World Scientific, New Jersey, 2008).

    Google Scholar 

  4. F. Y. Wu, The Potts Model, Rev. Mod. Phys. 54, 235–268 (1982).

    Article  Google Scholar 

  5. W. Zhang and Y. Deng, “Monte Carlo study of the triangular lattice gas with first- and second-neighbor exclusions,” Phys. Rev. E 78, 031103 (2008).

    Article  Google Scholar 

  6. R. Masrour and A. Jabar, “Magnetic properties of mixed spin-5/2 and spin-2 Ising model on a decorated square lattice: a Monte Carlo simulation,” Phys. A 515, 270–278 (2019).

    Article  Google Scholar 

  7. R. Masrour and A. Jabar, “Magnetic properties in stacked triangular lattice: Monte Carlo approach,” Phys. A 491, 926–934 (2018).

    Article  CAS  Google Scholar 

  8. S. E. Korshunov, “Phase transitions in two-dimensional systems with continuous degeneracy,” Phys. Usp. 49, 225–262 (2006).

    Article  CAS  Google Scholar 

  9. A. Malakis, P. Kalozoumis, and N. Tyraskis, “Monte Carlo studies of the square Ising model with next-nearest-neighbor interactions,” Eur. Phys. J. B 50, 63–67 (2006).

    Article  CAS  Google Scholar 

  10. S. S. Sosin, L. A. Prozorova, and A. I. Smirnov, “New magnetic states in crystals,” Phys. Usp. 48, 83–90 (2005).

    Article  CAS  Google Scholar 

  11. M. Kazuaki and O. Yukiyasu, “Dynamical scaling analysis of symmetry breaking for the antiferromagnetic triangular Heisenberg model in a uniform magnetic field,” Phys. Rev. B 101, 184427(7) (2020).

  12. A. K. Murtazaev, M. K. Ramazanov, D. R. Kurbanova, M. A. Magomedov, and K. Sh. Murtazaev, “Phase diagrams and ground-state structures of the antiferromagnetic materials on a body-centered cubic lattice,” Mater. Lett. 236, 669–671 (2019).

    Article  CAS  Google Scholar 

  13. M. K. Ramazanov and A. K. Murtazaev, “Phase diagram of the antiferromagnetic Heisenberg model on a cubic lattice,” JETP Lett. 109, 589–593 (2019).

    Article  CAS  Google Scholar 

  14. A. K. Murtazaev, M. K. Ramazanov, and M. K. Badiev, “Phase transitions in the Ising model on a triangular lattice with different values of interlayer exchange interaction,” Low Temp. Phys. 45, 1263–1266 (2019).

    Article  CAS  Google Scholar 

  15. M. K. Badiev, A. K. Murtazaev, M. K. Ramazanov, and M. A. Magomedov, “Critical properties of the Ising model in a magnetic field,” Low Temp. Phys. 46, 693 (2020).

    Article  Google Scholar 

  16. A. K. Murtazaev, D. R. Kurbanova, and M. K. Ramazanov, “Phase transitions and critical properties of the Heisenberg antiferromagnetic model on a body-centered cubic lattice with second nearest neighbor interaction,” J. Exp. Theor. Phys. 129, 903–910 (2019).

    Article  CAS  Google Scholar 

  17. M. Nauenberg and D. J. Scalapino, “Singularities and scaling functions at the Potts-model multicritical point,” Phys. Rev. Lett. 44, 837–840 (1980).

    Article  CAS  Google Scholar 

  18. J. L. Cardy, M. Nauenberg, and D. J. Scalapino, “Scaling theory of the Potts-model multicritical point,” Phys. Rev. B 22, 2560–2568 (1980).

    Article  CAS  Google Scholar 

  19. M. K. Ramazanov, A. K. Murtazaev, and M. A. Magomedov, “Phase diagrams and ground-state structures of the Potts model on a triangular lattice,” Phys. A 521, 543–550 (2019).

    Article  Google Scholar 

  20. H. Feldmann, A. J. Guttmann, I. Jensen, R. Shrock, and S.-H. Tsai, “Study of the Potts model on the honeycomb and triangular lattices: Low-temperature series and partition function zeros,” J. Phys. A 31, 2287–2310 (1998).

    Article  Google Scholar 

  21. F. A. Kassan-Ogly and A. I. Proshkin, “Frustrations and ordering in magnetic systems of various dimensions,” Phys. Solid State 60, 1090–1097 (2018).

    Article  CAS  Google Scholar 

  22. A. K. Murtazaev, M. K. Ramazanov, M. K. Mazagaeva, and M. A. Magomedov, “Phase transitions and thermodynamic properties of the Potts model with spin states number q = 4 on a hexagonal lattice,” J. Exp. Theor. Phys. 129, 421–425 (2019).

    Article  CAS  Google Scholar 

  23. A. K. Murtazaev, D. R. Kurbanova, and M. K. Ramazanov, “Phase transitions and the thermodynamic properties of the Potts model with the number of spin states q = 4 on a triangular lattice,” Phys. Solid State 61, 2172–2176 (2019).

    Article  CAS  Google Scholar 

  24. M. K. Ramazanov, A. K. Murtazaev, M. A. Magomedov, and M. K. Mazagaeva, “Phase transformations and thermodynamic properties of the potts model with q = 4 on a hexagonal lattice with interactions of next-nearest neighbors,” Phys. Solid State 62, 499–503 (2020).

    Article  CAS  Google Scholar 

  25. M. G. Townsend, G. Longworth, and E. Roudaut, “Triangular-spin, kagome plane in jarosites,” Phys. Rev. B 33, 4919–4926 (1986).

    Article  CAS  Google Scholar 

  26. Y. Chiaki and O. Yutaka, “Three-dimensional antiferromagnetic q-state Potts models: application of the Wang–Landau algorithm,” J. Phys. A: Math. Gen. 34, 8781–8794 (2001).

    Article  Google Scholar 

  27. A. K. Murtazaev, F. A. Kassan-Ogly, M. K. Ramazanov, and K. Sh. Murtazaev, “Study of phase transitions in the antiferromagnetic Heisenberg model on a body-centered cubic lattice by Monte Carlo simulation,” Phys. Met. Metallogr. 121, 346–351 (2020).

    Article  Google Scholar 

  28. A. K. Murtazaev, D. R. Kurbanova, and M. K. Ramaza-nov, “Phase diagram of the antiferromagnetic Heisenberg model on a bcc lattice with competing first and second neighbor interactions,” Phys. A 545, 123548(6) (2020).

  29. A. K. Murtazaev, F. A. Kassan-Ogly, M. L. Ramazanov, and K. Sh. Murtazaev, “Phase diagram of the antiferromagnetic Potts model with number q = 4 of spin states in the hexagonal lattice,” Phys. Met. Metallogr. 122, 428–433 (2021).

    Article  CAS  Google Scholar 

  30. A. Mitsutake, Y. Sugita, and Y. Okamoto, “Generalized-ensemble algorithms for molecular simulations of biopolymers,” Biopolymers (Pept. Sci.) 60, 96–123 (2001).

  31. F. Wang and D. P. Landau, “Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram,” Phys. Rev. E 64, 056101–1–056101–16 (2001).

    Google Scholar 

  32. F. Wang and D. P. Landau, “Efficient, multiple-range random walk algorithm to calculate the density of states,” Phys. Rev. Lett. 86, 2050–2053 (2001).

    Article  CAS  Google Scholar 

  33. F. A. Kassan-Ogly, B. N. Filippov, A. K. Murtazaev, M. K. Ramazanov, and M. K. Badiev, “Influence of field on frustrations in low-dimensional magnets,” J. Magn. Magn. Mater. 24, 3418–3421 (2012).

    Article  Google Scholar 

  34. F. A. Kassan-Ogly, A. K. Murtazaev, A. K. Zhuravlev, M. K. Ramazanov, and A. I. Proshkin, “Ising model on a square lattice with second-neighbor and third- neighbor interactions,” J. Magn. Magn. Mater. 384, 247–254 (2015).

    Article  CAS  Google Scholar 

  35. A. I. Proshkin and F. A. Kassan-Ogly, “Frustration and phase transitions in Ising model on decorated square lattice,” Phys. Met. Metallogr. 120, 1366–1372 (2019).

    Article  CAS  Google Scholar 

  36. F. A. Kassan-Ogly and A. I. Proshkin, “Ising model on planar decorated lattices. Frustrations and their influence on phase transitions,” Phys. Met. Metallogr. 120, 1359–1365 (2019).

    Article  CAS  Google Scholar 

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Funding

This study was performed within the state task from the Ministry of Education and Science of Russia (project no. AAAA-A19-119051490043-5).

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Authors and Affiliations

  1. Institute of Physics, Dagestan Federal Research Center, Russian Academy of Sciences, 367003, Makhachkala, Russia

    M. K. Ramazanov, M. A. Magomedov, M. K. Mazagaeva & A. A. Murtazaeva

  2. Dagestan Federal Research Center, Russian Academy of Sciences, 367000, Makhachkala, Russia

    A. K. Murtazaev

Authors
  1. M. K. Ramazanov
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  2. A. K. Murtazaev
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  3. M. A. Magomedov
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  4. M. K. Mazagaeva
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  5. A. A. Murtazaeva
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Corresponding author

Correspondence to M. K. Ramazanov.

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Translated by E. Glushachenkova

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Ramazanov, M.K., Murtazaev, A.K., Magomedov, M.A. et al. Studying the Effect of Strong Magnetic Fields on the Phase Transitions of the Frustrated Potts Model with a Number of Spin States q = 4. Phys. Metals Metallogr. 123, 290–296 (2022). https://doi.org/10.1134/S0031918X22030085

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