In the early 90s several groups studied the statistical properties of lattice gravity models based on the Regge calculus.
I wrote several programs for this purpose and decided to publish them here, just in case somebody finds the behavior
of those models as interesting as I do. A simulation which used to take months on a supercomputer can now
be finished in a few hours on the laptop of a hobbyist.
The source code shows its age of 20+ years, but is relatively simple and can be easily compiled on a command line
without project files or special header files or libraries.
Please feel free to use them as you wish, however, if you want to use the code for research you should probably contact
me, so that I can explain some of the details.
tom.c is used to triangulate the 4-sphere and needs two numbers as input: The number of bsd steps (0 to 380) and
a random seed.
marc.c uses the triangulation files created by tom to perform the simulation and minp.txt contains reasonable
parameters for a simulation run.
rex.f performs triangulation and simulation for the 4-torus with input file rinp.txt.
Some results ...
The chart below depicts XR with fixed sigma and lambda and varying beta for increasing number of vertices.
The increasing peak suggests a phase transition.
The correlation between links at increasing distance d near a critial point. Notice the "wavelength" = 5 and
the strong (anti)correlation for large d ...