English

On the free energy within the mean-field approximation

Statistical Mechanics 2009-11-11 v1 Materials Science

Abstract

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.

Keywords

Cite

@article{arxiv.cond-mat/0601125,
  title  = {On the free energy within the mean-field approximation},
  author = {R. Agra and F. van Wijland and E. Trizac},
  journal= {arXiv preprint arXiv:cond-mat/0601125},
  year   = {2009}
}

Comments

pedagogical paper for undergraduate teaching, to appear in Eur. J. Physics