Skip to main content
SpringerLink
Log in

Frustration and Phase Transitions in Ising Model on Decorated Square Lattice

  • Published:
Physics of Metals and Metallography Aims and scope Submit manuscript

Abstract

The Ising model on a square lattice with arbitrary number of decorating spins, considering both the interactions between nodal and decorating spins is examined. A plethora of peculiarities such as heat capacity splitting, generation and suppression of multiple phase transitions and several kinds of partial ordering are thoroughly scrutinized. A rigorous analytical expression for the partition function closely resembling the one obtained by Onsager is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

Similar content being viewed by others

REFERENCES

  1. L. Onsager, “Crystal statistics. I. A two-dimensional model with an order–disorder transformation,” Phys. Rev. 65, 117–149 (1944).

    Article  CAS  Google Scholar 

  2. R. M. F. Houtappel, “Order–disorder in hexagonal lattices,” Physica 16, 425–455 (1950).

    Article  Google Scholar 

  3. G. H. Wannier, “Antiferromagnetism. The triangular Ising net,” Phys. Rev. 79, 357–364 (1950).

    Article  Google Scholar 

  4. K. Kanô and S. Naya, “Antiferromagnetism. The kagomé Ising net,” Prog. Theor. Phys. 10, 157–172 (1953).

    Article  Google Scholar 

  5. D. P. Landau and K. Binder, A Guide to Monte-Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, 2009.

    Book  Google Scholar 

  6. A. K. Murtazaev, M. K. Ramazanov, and M. K. Badiev, “Critical properties of the two-dimensional Ising model on a square lattice with competing interactions,” Phys. B: Condens. Matter 476, 1–5 (2015).

    Article  CAS  Google Scholar 

  7. H. T. Diep, Frustrated spin systems (World Scientific, Singapore, 2013).

    Book  Google Scholar 

  8. F. Y. Wu, “The Potts model,” Rev. Mod. Phys. 54, 235–268 (1982).

    Article  Google Scholar 

  9. I. Syozi and S. Miyazima, “A statistical model for the dilute ferromagnet,” Prog. Theor. Phys. 36, 1083–1094 (1966).

    Article  CAS  Google Scholar 

  10. M. Fisher, “Transformations of Ising models,” Phys. Rev. 113, 969–981 (1958).

    Article  Google Scholar 

  11. M. Jaščur, V. Štubňa, K. Szalowski, and T. Balcerzak, “Frustration in an exactly solvable mixed-spin Ising model with bilinear and three-site four-spin interactions on a decorated square lattice,” J. Magn. Magn. Mater. 417, 92–99 (2016).

    Article  Google Scholar 

  12. L. Čanova, J. Strečka, and M. Jaščur, “Exact results of the mixed-spin Ising model on a decorated square lattice with two different decorating spins of integer magnitudes,” Int. J. Mod. Phys. B 22, 2355–2372 (2008).

    Article  Google Scholar 

  13. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, New York, 1982).

    Google Scholar 

  14. H. A. Kramers and G. H. Wannier, “Statistics of the two-dimensional ferromagnet. Part I,” Phys. Rev. 60, 252–262 (1941).

    Article  Google Scholar 

  15. 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 

  16. I. Syozi, “A decorated Ising lattice with three transition temperatures,” Prog. Theor. Phys. 39, 1367–1368 (1968).

    Article  Google Scholar 

  17. 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. 324, 3418–3421 (2012).

    Article  CAS  Google Scholar 

  18. J. F. Counsell, R. M. Dell, A. R. Junkison, and F. F. Martin, “Thermodynamic properties of uranium compounds,” Trans. Faraday Soc. 63, 72–79 (1966).

    Article  Google Scholar 

  19. A. Blaise, R. Lagnier, J. E. Gordon, and R.Troc, “Heat capacity studies of ThP and UP0.5As0.5 solid solution. Reanalyzing UP data,” J. Low-Temp. Phys. 61, 323–335 (1985).

    Article  CAS  Google Scholar 

  20. H. Yokokawa, Y. Takahashi, and T. Mukaibo, “The heat capacity of uranium monophosphide from 80 to 1080 K and the electronic contribution,” in Thermodynamics of Nuclear Materials 1974, Vol. II (Int. Atomic Energy Agency, Vienna, 1975), pp. 419–430.

  21. A. Blaise, R. Troc, R. Lagnier, and M. J. Mortime, “The heat capacity of uranium monoarsenide,” J. Low. Temp. Phys. 38, 79–92 (1980).

    Article  CAS  Google Scholar 

Download references

Funding

The research was carried out within the state assignment of Minobrnauki of Russia (theme “Quantum” no. AAAA-A18-118020190095-4), supported in part by Ural Branch of the Russian Academy of Sciences (project no. 18-2-2-11).

Author information

Authors and Affiliations

  1. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 620108, Ekaterinburg, Russia

    A. I. Proshkin & F. A. Kassan-Ogly

  2. Ural Federal University Named after the first President of Russia B.N. Yeltsin, 620002, Ekaterinburg, Russia

    A. I. Proshkin

Authors
  1. A. I. Proshkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. A. Kassan-Ogly
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Proshkin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Proshkin, A.I., Kassan-Ogly, F.A. Frustration and Phase Transitions in Ising Model on Decorated Square Lattice. Phys. Metals Metallogr. 120, 1366–1372 (2019). https://doi.org/10.1134/S0031918X19130234

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0031918X19130234

Keywords:

Search

Navigation