- \displaystyle M & = \frac{1}{Z} \sum_{\{S\}} (\sum_{i} \mu S_i) e^{-\beta H} \\[2mm]
- \displaystyle & = \frac{1}{\beta} (\frac{\partial}{\partial{B_0}} \, \textrm{ln} \, Z) \\[2mm]
- \displaystyle & \stackrel{N >> 1}{\longrightarrow} \frac{N}{\beta \lambda_+} \frac{\partial{\lambda_+}}{\partial{B_0}} \\[2mm]
+ \displaystyle M & \displaystyle = \frac{1}{Z} \sum_{\{S\}} (\sum_{i} \mu S_i) e^{-\beta H} \\[2mm]
+ \displaystyle & \displaystyle = \frac{1}{\beta} (\frac{\partial}{\partial{B_0}} \, \textrm{ln} \, Z) \\[2mm]
+ \displaystyle & \displaystyle \stackrel{N >> 1}{\longrightarrow} \frac{N}{\beta \lambda_+} \frac{\partial{\lambda_+}}{\partial{B_0}} \\[2mm]