##
Useful Programs and Formulas

###
of

##
H. Kleinert and
V. Schulte-Frohlinde

*Critical Properties of Phi^4 Theories*

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

1.
Renormalization Constants
and
renormalization group functions
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)

(Mathematica .m format)

2.
Renormalization Group Functions in Phi^4 Theories
with O(N)-Symmetric and Cubic Interactions.

Expansions in powers of the coupling constants

Results of

H. Kleinert and V. Schulte-Frohlinde

Phys. Lett. B **342**, 284 (1995) (cond-mat/9503038)

(Mathematica .m format)

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
Results of

H. Kleinert and V. Schulte-Frohlinde

Phys. Lett. B **342**, 284 (1995) (cond-mat/9503038)

(Mathematica .m format)

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 $N=0,1,2,3$.

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(unpublished).

(Mathematica .m format)

The unpublished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
by

P. Butera and M. Comi (hep-lat/9703018).

(Mathematica .m format)

6.
Mathematica Program to Generate all Feynman Diagrams of phi^4-Theory up to Six Loops
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).

(Mathematica .m format)

OUTPUT
OF THIS PROGRAM

Click on this line for detailed explanation of program and usage!

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