The phase transition of the 2d-ising model by using monte carlo method

الملخص EN

-In this project, the location of the phase transition in the two dimensional Ising model will be determined using Monte Carlo simulation with importance sampling.

The magnetization per site [m], energy per site [J], magnetic susceptibility, specific heat of a Ferromagnetic materials are Calculated as a function of temperature T for 10 ͯ 10, 20 ͯ 20, 40 ͯ 40, 50 ͯ 50 spin lattice interaction by using Monte Carlo Simulation of the 2D Ising Model for some experimental values of ferromagnetic materials such as Gadolinium Chloride (GdCl 3) at Curie temperature TC= 2.2 J kB , and ferromagnetic thin film from Nickel (Ni ) growth on cooper (Cu)at Curie temperature TC= 2.772 J kB , in zero and nonzero magnetic field.

It was noticed that above a certain temperature (Tc) the material will be in a paramagnetic state, this will lead to that the average magnetization will be decrease and the average energy increase, while below that temperature, it will be in a ferromagnetic state, and the average magnetization will increase and the average energy decrease.

Moreover, above a certain temperature spontaneous magnetization will be zero.