On the free energy within the mean-field approximation

Details On the free energy within the mean-field approximation On the free energy within the mean-field approximation

2006-01-06

arxiv.org/abs/cond-mat/0601125v1

European Journal of Physics 27, 407 (2006).

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/0143-0807/27/2/022

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.

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