Multiplicity function for N noninteracting spins
（重定向自Multiplicity function）
The multiplicity function for a two state paramagnet, W(n,N), is the number of spin states such that n of the N spins point in the z-direction. This function is given by the combinatoric function C(N,n). That is:
![W (n,N) = {N \choose n} = {{N!} \over {n!(N - n)!}}](/Images/godic/202501/28/5bae8499b873e1254bc55229ac44291c1442.png")
It is primarily used in introductory statistical mechanics and thermodynamics textbooks to explain the microscopic definition of entropy to students. If the spins are non-interacting, then the multiplicity function counts the number of states which have the same energy in an external magnetic field. By definition, the entropy S is then given by the natural logarithm of this number: