A mean field method with correlations determined by linear response
  We introduce a new mean-field approximation based on the reconciliation of maximum entropy and linear response for correlations in the cluster variation method. Within a general formalism that includes previous mean-field methods, we derive formulas improving upon, e.g., the Bethe approximation and the Sessak-Monasson result at high temperature. Applying the method to direct and inverse Ising problems, we find improvements over standard implementations. 
Jack Raymond and Federico Ricci-Tersenghi
cond-mat.stat-mech cond-mat.dis-nn