The Convergence Of Cluster Expansion For Partition Function

According to the general principles of equilibrium statistical mechanics, in principle, the thermodynamic properties of any system can be calculated, however, for the real thermodynamic systems, strictly analytical calculations are extremely difficult because of the large number of particles and existing interaction between particles, so "approximate calculation method" must be used. Group expansion method is an approximate method, this method of partition function first to do the group commenced, next to do approximation processing.Any approximation method, we must specify its approximate condition, that is the scope of application. It is an important part of the approximation theory that discussing the impact on the approximation and the applicable scope of the approximation method about physical properties. Properties of thermodynamic system are calculated approximately by group expansion method, this need to make a truncation calculation with group series, however the premise of the truncated calculation is the group series has a good convergence.Through numerical calculation, this paper compared the size of the adjacent item, researched the convergence properties of the series in the group. Specifically, we studied the influence on the convergence properties from the number of particle and the density of particle, the intensity of interaction between particles, interaction process and the particle size in the system.The results show that:in statistical mechanics, due to the difficulties arising from the large number of particles, It is still an important factor to affect the application of this method in the approximation of the group.It has a better convergence only when the total number of particles is extremely small or when the number of particles is large and there must be very weak interaction.