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The Phase Transition of the 2D-Ising Model By Using Monte Carlo Method

Sa`ad. N. Abood --- Dhia'a Khalid Kudeer

Engineering and Technology Journal مجلة الهندسة والتكنولوجيا
ISSN: 16816900 24120758 Year: 2011 Volume: 29 Issue: 2 Pages: 261-277
Publisher: University of Technology الجامعة التكنولوجية

Abstract

In this project, the location of the phase transition in the two dimensional Isingmodel will be determined using Monte Carlo simulation with importance sampling.the magnetization per site [m ], energy per site [J ], magnetic susceptibility, specificheat of a Ferromagnetic materials are Calculated as a function of temperature T for10´10, 20´ 20, 40´ 40 , 50´50 spin lattice interaction by using Monte CarloSimulation of the 2D Ising Model for some experimental values of ferromagneticmaterials such as Gadolinium Chloride ( ) 3 GdCl at Curie temperaturec T B = 2.2 J k , and ferromagnetic thin film from Nickel ( ) i N growth oncooper (Cu)at Curie temperature c B T = 2.772 J k , in zero and nonzero magneticfield. It was noticed that above a certain temperature ( ) c T the material will be in aparamagnetic state, this will lead to that the average magnetization will be decreaseand the average energy increase, while below that temperature ,it will be in aferromagnetic state, and the average magnetization will increase and the averageenergy decrease. Moreover, above a certain temperature spontaneous magnetizationwill be zero

Keywords

Monte Carlo methods --- the XYmodel