The Julia codes are parallelized on the available cores. It is therefore advisable for the performance to parallelize the codes keeping into account the number of CPU cores present on the system.

A full list of the employed Julia packages can be found in ./inc/pkgs.jl. Before executing the source codes, all packages must be installed.

The Julia's Just-in-Time compiler is such that the first execution of functions is considerably slower that following ones, and it also allocates much more memory. To avoid this, you can use the DaemonMode package.

To execute the Julia codes (on a single machine with the synthax below) you can run the following command:

$JULIA_EXECUTABLE_PATH   -p   [N-1]    $JULIA_CODE_PATH   $ARGS

where [N-1] is the number of workers. The ARGS parameter depends on the specific kind of computation. We show an example below.

ARGS = DATA_SL2CFOAM_FOLDER    CUTOFF    JB    DL_MIN    DL_MAX     IMMIRZI    STORE_FOLDER    MONTE_CARLO_ITERATIONS    NUMBER_OF_TRIALS

where:

• DATA_SL2CFOAM_FOLDER: folder with fastwigxj tables where boosters (and possibly vertices) are retrieved/stored

• CUTOFF: the maximum value of bulk spins

• JB: value of boundary spins

• DL_MIN: minimum value of truncation parameter over auxiliary spins

• DL_MAX: maximum value of truncation parameter over auxiliary spins

• IMMIRZI: value of Immirzi parameter

• STORE_FOLDER: folder where data are saved

• MONTE_CARLO_ITERATIONS: number of monte carlo sampling for each trial

• NUMBER_OF_TRIALS: number of trials

Additionally, you can specify the weights $\mu_1, \mu_2 \dots \mu_n$ on bulk faces inside the code script, with the vector FACE_WEIGHTS_VEC. Each bulk face with spin $j$ has dimension $(2j+1)^{\mu}$, and the code computes all amplitudes with provided weights.