Published March 1, 2006
| Version v1
Journal article
On the free energy within the mean-field approximation
- 1. Laboratoire de Physique Theorique (UMR 8627 du CNRS), Batiment 210, Universite Paris-Sud, 91405 Orsay (France)
- 2. Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Batiment 100, Universite Paris-Sud, 91405 Orsay (France)
Description
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 anti-ferromagnetic 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
Availability note (English)
Available online at http://stacks.iop.org/0143-0807/27/407/ejp6_2_022.pdf or at the Web site for the journal European Journal of Physics (ISSN 1361-6404) http://www.iop.org/Additional details
Identifiers
- URL
- http://stacks.iop.org/0143-0807/27/407/ejp6_2_022.pdf;
- DOI
- 10.1088/0143-0807/27/2/022;
- PII
- S0143-0807(06)12481-2;
Publishing Information
- Journal Title
- European Journal of Physics
- Journal Volume
- 27
- Journal Issue
- 2
- Journal Page Range
- p. 407-412
- ISSN
- 0143-0807
- CODEN
- EJPHD4
INIS
- Country of Publication
- United Kingdom
- Country of Input or Organization
- International Atomic Energy Agency (IAEA)
- INIS RN
- 37053306
- Subject category
- S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
- Descriptors DEI
- ANTIFERROMAGNETISM; APPROXIMATIONS; FAILURES; FREE ENERGY; ISING MODEL; MEAN-FIELD THEORY; MINIMIZATION; VARIATIONAL METHODS
- Descriptors DEC
- CALCULATION METHODS; CRYSTAL MODELS; ENERGY; MAGNETISM; MATHEMATICAL MODELS; OPTIMIZATION; PHYSICAL PROPERTIES; THERMODYNAMIC PROPERTIES