text: p| 
  
  k )λ2  j + τ x 
  
  (Sk3 
  Sk4)(1 
  × 
  · 
  Hcluster k]−1 
  Hcluster j − 
  Sj4) 
  · 
  We can use the previous argument for both cluster j and 
  k, so (1 
  −Pjk) can be 
  −PAB)[0 
  2Jcluster)−1. This term becomes 
  replace by c-number ( 
  
  − Pjk) 
  
  Hcluster j − 
  − 
  
  r λ2 
  Hmagnetic =  Hcluster j + 
  2Jcluster Pjk[Sj2 
  (Sk3  Sk4)][Sk2  (Sj3  Sj3)] 
  Pjk. 
  X 
  j  X 
  x−links <jk> 
  −  ·  ×  ·  × 
  
  Spin rotation symmetry again helps to separate the terms 
  j τ z 
  τ z 
  k . 
  for cluster j and k, and we get 
  · 
  The other cross term r λ2 
  Sj4)(1 
  (Sk3 
  Hcluster j − 
  
  +  λyHperturbation y 
  X 
  y−links <jk> 
  
  − 
  PjkSk2 
  Hcluster k]−1(1 
  +  λzHperturbation z 
  
  − 
  × 
  X 
  z−links <jk> 