A Monte Carlo Simulation Of Non-equilibrium Steady State Of2D Ising Model

The application of Ising Model is now related to physics, chemistry, biology, etc. Obviously more and more attention has been paid to it. It is well known that it is very convenient to study the Ising Model through Monte Carlo simulations. So it is very interesting and important if the Monte Carlo simulation can be expanded to study the non-equilibrium steady state of Ising Model.In this thesis, the local temperature of non-equilibrium steady state is defined through the local equilibrium, then the characters of this steady state of the two dimensional Ising model which is confined in a temperature gradient are studied by Monte Carlo simulations, and the energy, heat capacity, spin ratio, magnetization and magnetic susceptibility of the system are determined. It is found that the energy and magnetization of the system are continuous, but the heat capacity and magnetic susceptibility will have a peak or a sharp jump at the reduced temperature of2.3. Obviously, it is the critical temperature of phase transition, and it is in good agreement with the theoretical prediction. In addition, the influence on the Ising model system from the magnetic field and the strength of coupling among the lattices are studied respectively. The numerical results show that the critical temperature will be enlarged by the magnetic field, and the critical temperature will be also enlarged if the coupling strength is increased.Based on the results obtained in our study, we hope that the idea and the results will provide useful information for those who will make a further study on the Ising model.