On the free energy within the mean-field approximation

R. Agra ¹, F. van Wijland ¹, E. Trizac ²

European Journal of Physics 27 (2006) 407-412

We compare two widespread formulations of the mean-field approximation, based on minimizing an appropriately built mean-field free energy. We use the example of the antiferromagnetic Ising model to show that one of these formulations does not guarantee the existence of an underlying variational principle. This results in a severe failure where straightforward minimization of the corresponding mean-field free energy leads to incorrect results.

• 1. Laboratoire de Physique Théorique d’Orsay (LPT),
  CNRS : UMR8627 – Université Paris XI – Paris Sud
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud