Nanomeghyas

Nanomeghyas

Construction of phase diagrams in anisotropic nanoscaled Ising thin films with diluted surfaces using cellular automata approach

Document Type : Original Article

Authors
1 Faculty of Chemistry, Kharazmi University, Tehran, Iran
2 Faculty of Chemistry ,, Kharazmi University, Tehran, Iran
Abstract
The phase diagrams of the anisotropic three-layer Ising model on the square lattice with diluted surfaces have been constructed with high precision, using the probabilistic cellular automata with the Glauber algorithm. The thermal variation of magnetization is calculated for different values of nearest neighbor couplings: namely J ≠  Js  ≠  J1, where J and Js  are the nearest neighbor  couplings within inner-layer and surface-layer, respectively, and each magnetic site in the surface-layer is coupled with the nearest site in the inner-layer via the exchange interaction J1. In the case of the antiferromagnetic coupling between layers, simulation results show existence of the compensation point in the phase diagram.  

 
[1] E. Ising, “Beitrag zur Theorie des Ferromagnetismus,” Z. Phys. 31, 253-258, 1925.
[2] L. Onsager, Crystal Statistics. I. “A two dimensional model with an order-disorder transition,” Phys. Rev. 65, 117-149, 1944.
[3] R. Honmura, T. Kaneyoshi, “Contribution to the new type of effective-field theory of the Ising model,” J. Phys. C. Solid. State. 12, 3979-3992, 1979.
[4] T. Kaneyoshi, “Differential operator technique in the Ising spin systems,” Acta. Phys. Pol. A. 83, 703-737, 1993.
[5] T. Kaneyoshi, “Phase diagrams in nanoscaled Ising thin films with diluted surfaces; effects of interlayer coupling at the surfaces,” Physica. B. 408, 126-133, 2013.
[6] M. Ghaemi, “Cellular Automata simulation of two-layer Ising and Potts models, in: A. Salcido (Eds.), Cellular Automata-Simplicity Behind Complexity,” InTech Publisher, India, pp. 439-456, 2011.
[7] T. Kaneyoshi, “Introduction to Surface Magnetism,” CRC Press, USA, 1991.
[8] R. N. Bhowmik, “Evidence of ferrimagnetism in ferromagnetic La0.67Ca0.33MnO3 nanoparticle,” J. Magn. Magn. Mater. 323, 311-315, 2011.
[9] Y. Asgari, M. Ghaemi, “Obtaining critical point and shift exponent for the anisotropic two-layer Ising and Potts models: Cellular automata approach,”  Physica. A. 387, 1937-1946, 2008.
[10] Y. Asgari, M. Ghaemi, M. G. Mahjani, “Calculation of the critical point for two-layer Ising and Potts models using Cellular Automata,” Lect. Notes. Comput. Sc. 3305, 709-718, 2004.
[11] M. Ghaemi, S. Ahmadi, “Calculation of critical properties for the anisotropic two-layer Ising model on the Kagome lattice: Cellular automata approach,” Physica. A. 391, 2007-2013, 2012.
[12] R. J. Glauber, “Time-dependent statistics of the Ising model,” J. Math. Phys. 4, 294-307, 1963.
[13] M. E. Newman, G. T. Barkema, “Monte Carlo Methods in Statistical Physics,” first ed., Oxford University Press, New York, 2001.

  • Receive Date 29 January 2021
  • Revise Date 31 May 2021
  • Accept Date 08 July 2021