| Issue |
Europhys. Lett.
Volume 49, Number 6, March 2000
|
|
|---|---|---|
| Page(s) | 801 - 806 | |
| Section | Condensed matter: electronic structure, electrical, magnetic, and optical properties | |
| DOI | https://doi.org/10.1209/epl/i2000-00222-0 | |
| Published online | 01 September 2002 | |
Dynamical mean-field theory as a random loop problem
Institute of Physics, Dortmund University - D-44221 Dortmund, Germany
Received:
11
October
1999
Accepted:
5
January
2000
In dynamical mean-field theory (DMFT) the Anderson lattice model is mapped
onto the impurity model, with the density of states determined from a self-consistence condition
(scc). The mapping is rigorous in infinite spatial dimensions d. It can be diagrammatically modelled as self-avoiding loops.
While at finite d > 4 the number of mathematical self-avoiding loops is
negligible compared to all random loops, to the mathematical scc at infinite d they contribute a
fraction 1/e to all random loops. The limits of 
and infinite loop length cannot be interchanged, thus making
1/d-corrections to the scc questionable. We find the analogous result for the
DMFT loop. We also discuss numerical difficulties arising in the infinite-U limit of the Anderson
lattice model, and analytically simulate them.
PACS: 75.20.Hr – Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EDP Sciences, 2000
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.