TwoDimensional IsingModel ApplicationWith MONTE CARLO Method

Abstract

The location of the phase transition in the two dimensional Ising model were determined using Monte Carlo simulation with importance sampling. The magnetization persite ,energy per site , magnetic susceptibility , specific heat of a Ferromagnetic materials were calculated as a function of temperature for spin lattice interaction in zero and nonzero magnetic field . There is thus a phase transition defined by the Curie temperature. The Monte Carlo method was used to check the results and to confirm the phase transition . The internal interaction results were found to be consistent with what was expected. As a magnetic field is applied, the spins tend to align with it for ˃ and its effect is not significant at a very high temperature because of the thermal agitation. For ˂ , the alignment of the spins is possible only if the amplitude of the field is big enough.

Keywords

• spin anisotropy
• monte carlo simulation
• the xy model
• ising model