Perturbation theory for selfavoiding walks and φ^{4} theory in Python
ParisiSourlas [1] and McKane [2] have expressed correlation functions
for selfavoiding walks in terms of a supersymmetric φ^{4}type field theory.
This has been surveyed in [3].
Brydges and Slade have developed a rigorous approach to study such field theories by
renormalisation group analysis.
The method depends on a certain explicit calculation (described in detail in [6], see also [5]).
The explicit calculation can be done by hand, for example using Feynman diagram mnemonics, but these calculations can become
tedious. The program below (written in the Python programming language)
does these computations automatically.

Perturbation theory for selfavoiding walks in Python (preliminary version)
requires Python 2.6 or higher

The results play a role in [8], [9] (which rely on
[6], [7] for control of the nonperturbative remainder).
Contents

wick.py is a collection of Python classes to handle the combinatorics involved in calculating Gaussian integrals
and their fermionic analogs. It cannot be executed by itself.

sawpt.py utilizes wick.py to compute the specific expressions for the supersymmetric selfavoiding walk field theory
as described in [6].

phi4npt.py similarly computes the specific expressions for the ncomponent φ^{4} model
as described in [9].
References
 G. Parisi and N. Sourlas, N.,
Selfavoiding walk and supersymmetry,
J. Phys. Lett. 41 (1980),
L403L406,
link (subscription required).
 A.J. McKane,
Reformulation of n → 0 models using anticommuting scalar fields,
Phys. Lett. A 76 (1980),
no. 1,
2224,
link (subscription required).
 D.C. Brydges, J.Z. Imbrie, and G. Slade, Functional integral
representations for selfavoiding walk, Probab. Surv. 6 (2009), 3461,
link.
 D.C. Brydges and G. Slade,
A renormalisation group method. II. Approximation by local polynomials,
Preprint, 2014.
 R. Bauerschmidt, D.C. Brydges and G. Slade,
A renormalisation group method. III. Perturbative analysis,
Preprint, 2014.
 D.C. Brydges and G. Slade,
A renormalisation group method. IV. Nonperturbative analysis of weakly selfavoiding walk,
Preprint, 2014.
 D.C. Brydges and G. Slade,
A renormalisation group method. V. A single renormalisation group step,
Preprint, 2014.
 R. Bauerschmidt, D.C. Brydges and G. Slade,
Logarithmic correction for the susceptibility of the 4dimensional weakly selfavoiding walk: a renormalisation group analysis,
Preprint, 2014.
 R. Bauerschmidt, D.C. Brydges and G. Slade,
Scaling limits and critical behaviour of the 4dimensional ncomponent φ^{4} spin model,
Preprint, 2014.