MFA [tex]\hat{A}\hat{B}\approx \hat{A}\langle\hat{B}\rangle+\hat{B}\langle\hat{A}\rangle-\langle\hat{A}\rangle\langle\hat{B}\rangle[/tex] What this mean physically? What we neglect here? If I calculate Neel temperature using this method [tex]T_N^{MFA}[/tex] and using RPA method [tex]T_N^{RPA}[/tex] is there some relation between those temperatures?
Perhaps a natural way to see the decomposition is if A and B are fluctuations around some mean, i.e. <A> = <B> = 0. Then you just have AB ~ 0, i.e. you are neglecting correlated fluctuations in A and B.