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International Letters of Chemistry, Physics and Astronomy
ILCPA Volume 15
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Ising Model Phase Transition Calculation for Ferro-Paramagnetic Lattice
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Ising Model Phase Transition Calculation for Ferro-Paramagnetic Lattice

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Abstract:

The position of the phase transition in the two dimensional Ising model were determined byusing Monte Carlo simulation in a quadratic for area of variable length with external magnetic fieldswitched off (B = 0). The magnetization (M) per site (µ), magnetic susceptibility (x) of aferromagnetic and paramagnetic materials were calculated as a function of temperature T for(20×20,40×40,60×60), (80×80,120×120,200×200) spin lattice interactions. Nearest neighborinteraction is assumed (i.e. each spin has 4 neighbors); uses periodic boundary conditions. The Curietemperature (Tc = 2.27 J/kB ) is determined by measuring the magnetic susceptibility at which theferromagnetic and paramagnetic undergoes a phase change from order to disorder. There is thus aphase transition defined by the Curie temperature. The Monte Carlo method were used to check theseresults and to confirm the phase transition. The data are analyzed using the Curie-Weiss law whichcontains the Curie temperature as a parameter.

Info:

Periodical:
International Letters of Chemistry, Physics and Astronomy (Volume 15)
Pages:
201-212
DOI:
https://doi.org/10.18052/www.scipress.com/ILCPA.15.201
Citation:
D.`a K. Khudier and N. I. Fawaz, "Ising Model Phase Transition Calculation for Ferro-Paramagnetic Lattice", International Letters of Chemistry, Physics and Astronomy, Vol. 15, pp. 201-212, 2013
Online since:
June 2013
Authors:
Dhia`a K. Khudier, Nabeil I. Fawaz
Keywords:
Ferromagnetic Materials, Magnetic, Monte Carlo Simulation
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Distribution:
Open Access

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This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

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[3] Robert Knegjens, Simulation of the 2D Ising Model, May 13, 2008.

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[5] Indrek Mandre, The ising model, Course project in simulation of physical processes, Tallinn University of Technology, Dept. of Physics, Tallinn 2008.

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[8] Tobin Fricke, Monte Carlo investigation of the Ising model, Taken on the 9th of March 2008, March 11, 2008.

[9] Jacques Kotze, Introduction to Monte Carlo methods for an Ising Model of a Ferromagnet, 3Mar (2008).

[10] Matthias Reggentin, Monte Carlo Methods in Physics Ising model and Metropolis Algorithm, reggentin@physik. hu-berlin. de, 01-16-2010. ‏ ( Received 19 May 2013; accepted 22 June 2013 ).

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