Spin magnetization ($M=n^{-1}{\sum }_{i=1}^n{S}_i$)

The spin magnetization is the average signed spin of a discrete spin system. For $S_i\in \{-1,1\}$, $k$ positive spins give $M=-1+2k/n$. Multiplying by the magnetic moment per spin and the spin density relates this dimensionless average to physical magnetization.