Two Dimensional Ising Model Application With MONTE CARLO Method

The location of the phase transition in the two dimensional Ising model weredetermined using Monte Carlo simulation with importance sampling. The magnetization (M) persite(LL ), energy(E) per site (J ), magnetic susceptibility (X) , specific heat (Cv) of aFerromagnetic materials were calculated as a function of temperature T for(16 * 16 , 30 * 30 , 55 * 55 ) spin lattice interaction in zero and nonzero magnetic field(B = 0,B ǂ 0). There is thus a phase transition defined by the Curie temperature. The MonteCarlo method was used to check the results and to confirm the phase transition . The internalinteraction results were found to be consistent with what was expected. As a magnetic field isapplied, the spins tend to align with it for T ˃TC and its effect is not significant at a very hightemperature because of the thermal agitation. For T ˂ C T , the alignment of the spins is possibleonly if the amplitude of the field is big enough.