Abstract: Maxwell-Boltzmann distribution has broad application prospect in statistical physics.

This distribu- tion gives the Boltzmann probability of any microstate of the system，so we

can calculate the statistical average of the macroscopic observation of the system.

However，most of the real calculations are hard to be done，due to the fact that the number of

all the possible microstates increases exponentially with the number of the lattice

sites. In this paper，we take the Ising model as an example，to introduce the evolution of the

possible microstates from the view of the Boltzmann probability，hence we only need to consider

the microstates with large Boltzmann probability. In this way，we study the ground-state energy per

site and magnetization per site as functions of temperature，in a two-dimensional Ising model.

Key words: Maxwell-Boltzmann distribution, Boltzmann probability, Ising model, statistical average