Hagen Kleinert
 Professor Dr. Dr. h.c. mult.
Useful Programs & Formulas

If you use any of these, please don't forget to cite the source!

1. Renormalization Constants (Mathematica .m format) and renormalization group functions
(Mathematica .m format) of Phi^4 Theories^ with O(N)-Symmetric Interactions.
Expansions in powers of the coupling constants
Results of
H. Kleinert, J. Neu, V. Schulte-Frohlinde, K.G. Chetyrkin, and S.A. Larin,
Phys. Lett. B 272, 39 (1991) (hep-th/9503230)

2. Renormalization Group Functions in Phi^4 Theories with O(N)-Symmetric and Cubic Interactions.
Expansions in powers of the coupling constants
(Mathematica .m format)
Results of
H. Kleinert and V. Schulte-Frohlinde
Phys. Lett. B 342, 284 (1995) (cond-mat/9503038)


3. Epsilon Expansions (epsilon=4-D) for Critical Exponents in Phi^4 Theories with O(N)-Symmetric
and Cubic Interactions around the nontrivial Fixed Points Heisenberg, Ising and Cubic;
also for Critical Number N_c of Field Components at which Stability Changes from Heisenberg to Cubic Fixed Point.
Expansions in powers of epsilon=4-D.
(Mathematica .m format)
Results of
H. Kleinert and V. Schulte-Frohlinde
Phys. Lett. B 342, 284 (1995) (cond-mat/9503038)


4. Expansion of g, eta, nu^(-1) in powers of bare coupling constant g0 in three dimensions. Six-loop results for all O(N), seven-loop results for $N=0,1,2,3$. (Mathematica .m format)
The general-$N$ results are from
S. A. Antonenko, A. I. Sokolov (hep-th/9803264),
the $N=0,1,2,3$-results from
D.B. Murray and B.G. Nickel, Univ. of Guelph preprint 1991 (unpublished).

The unpublished
B.G. Nickel, D.I. Meiron, and G.B. Baker, Univ. of Guelph preprint 1977
can be downloaded from this URL


5. High-Temperature expansions of O(N)-Symmetric Classical Heisenberg Model
(Mathematica .m format) by
P. Butera and M. Comi (hep-lat/9703018).


6. Mathematica Program to Generate all Feynman Diagrams of phi^4-Theory up to Six Loops
(Mathematica .m format) from
Recursive Graphical Construction of Feynman Diagrams
and Their Multiplicities in phi^4- and in phi^2A-Theory
Hagen Kleinert, Axel Pelster, Boris Kastening, M. Bachmann (hep-th/9907168) .
- OUTPUT OF THIS PROGRAM
Click on this line for detailed explanation of program and usage!

© by Hagen Kleinert 2018