The particles network is a grid of size 10 x 10 x 1 whith a space step size is \(h_0=h_1=h_2=1 \)

A particle P is linked to all particules Q of the network if \( Q \in V_P=\{\displaystyle M_{{ax}_k}(|P_x-Q_x|)<=h_k \} \).

The Heissenberg coeficient of all particles is set to \(J=0 \). Note that if \(J \neq 0 \) the Heissenberg coefficient of the particle P is \( J_{pp}= - \displaystyle \sum_{q \in V_P} J_{pq} \).

The stochastic function is the Îto model modelized by the boost normal law and with a noise rate \( \varepsilon = 0 \) for determinitic case.

The options are set in the options file.

The simulation is computed by the code

./stockmagnet_main.exe --options=options.txt run

The code generates 4 file's types within the output path :

the log file to print all the comments, warnings, errors and provided options .
the prefix-meanE.txt text file describes the mean of the total energy at each time : t \( \bar E(t) \) is at each line
for each trajectory computed (given by the array option simulations), it gives:
- prefix-Es-si.txt text file which describes the evolution of all the energies at each time : t \( E_{tot}\) \( E_{z}\) \( E_{dem} \) \( E_{h} \)
- prefix-mu-si.txt text file which describes the magnetic moment for the si-th simulation at each time : t \( \forall p \in [0,P[, \forall k \in [0,2], \mu^p_k(t) \) at each line. It means 3xP+1 values per line where P is the number of particles
- prefix-mu-si.xmf which describes the same file as above but for the paraview program. With paraview software use:
  - XDMF reader
  - add the glyph filter
  - add the annotateTimeFilter1 with dt in scale parameter
  - and click on the play animation button and set the options (framerate, max number of iterations...)
  - to save go to File->save animation to save the film or File-> save screenshot to save image

To plot the energies txt file use the gnuplot script :

set title 'Energy' 
set terminal png size 800,500 enhanced background rgb 'white'
set style increment default 
set style data linespoints 
set xrange [0:20]
set autoscale y
set xtic auto
set ytic auto
set xlabel 'Times'
set ylabel 'E'
set output 'Es.png'
plot 'grid10x10_J0_2000x001_stratonovichn-Es-s0_E.plot' using 1:2 title 'Etot' with lines , 'grid10x10_J0_2000x001_stratonovichn-Es-s0_E.plot' using 1:3 title 'ConstantZeeman' with lines , 'grid10x10_J0_2000x001_stratonovichn-Es-s0_E.plot' using 1:4 title 'Demagnetized' with lines , 'grid10x10_J0_2000x001_stratonovichn-Es-s0_E.plot' using 1:5 title 'Heissenberg' with lines 

The obtained results are as follow:

aa href="../examples/Grid10x10x1/Doc/Es.png"> >
the energy evolution	the magnetic momenet evolution