Study On Temperature Distribution In Ising Model With Fixed Boundary Temperature

The developing computer simulation technology makes great help for us to understand the evolutionary and characteristics of the physical world.In this thesis,with the aid of Monte Carlo simulation,the Ising model near to its critical temperature has been studied in the following two aspects:the first one is that,for a given temperature distribution,the effective local region size has been determined by taken a series of local regions with different sizes into consideration.The result show that when a local temperature is far from the critical temperature,the calculation results are almost unaffected by the size of the local region.When the local temperature of a studied local region is near to the critical point,the difference between the calculated results will be very large if the local region size is very small,but this difference will be reduced quickly when the local region size is enlarge,and the calculation results will tend to be the same when the local region size is large than a certain value.Obviously,it is just the effective local region size.Another aspect is that,.based on the principle of equality flow of every local region,for a steady state,the temperature distribution of Ising model system with a boundary condition of fixed temperatures has been determined.The results show that,from the constant temperature of the boundary to the critical temperature,the temperature is almost linear,while near the critical point the temperature remains unchanged.In addition,the evolution of the temperature with time and all the physical quantities and their fluctuations are also obtained by the Monte Carlo simulations.It is waited in hope that the results about the effective local region and the temperature distribution may provide usefiul information for further investigations about Ising model.