A simple implementation of a Monte Carlo simulation of the classical Heisenberg model on a 2D or 3D lattice. It is possible to add also antisymmetric DMI interactions to simulate other type of systems.

The program use Numpy for the linear algebra and Numba jit compiler to accelerate the simulation.

The output can be viewed through a Jupyter notebook.

The configuration of the program is found in the file config.json. The important parameters to set are the number of processes (which should be equal to the number of the core of the computer), the number of step to be performed and the number of steps between two snapshots.

To run a set of simulations of a cubic system with cyclic boundary conditions you have to select a name for the set and a range of temperature and dimensions.

To initialize the set of system you have to run a command like:

$ ./set_simulation.py -i sim_816 -L 8,12,16 -T 0.5,3,0.25

This will create a set named sim_816 with dimensions 8, 12 and 16 and temperature ranging from 0.5 to 3 with steps of 0.25

To run the set:

$ ./set_simulation.py -r sim_816

Inside the ./simulation/sim_816 a directory for each ensemble will be created. Inside each one there will be saved four files:

• params.json Parameters of the simulation
• state.npy End state of the simulation
• snapshots_params.npy Parameters when the snapshosts were taken
• results.npy Energy and magnetization of each snapshot

To analyze the result, just run LT_set_analysis.ipynb in Jupiter.

It possible to continue the simulation with

$ ./set_simulation.py -r sim_816

the program will just take the end state as initial state and append the results to the old ones.

To generate a default lattice with given dimension just run

$ ./ dynamic_simulation.py -i sim_16 -d 16x16x16 -m 0,0,1

A simulation directory will be created inside ./simulations with a default parameter file and a initialized lattice of the given dimension with spin oriented toward z-axis.

To initialize a lattice of spin random oriented:

$ ./ dynamic_simulation.py -i sim_16 -d 16x16x16

To change dynamically the parameters, fill the param_J, param_D, param_Hz, param_T variables with an array of values. The simulation will proceed running a number of step equals to steps_number with each triplet of parameters in the arrays.

After have edit the parameters in the json file, you are ready to run the simulation with:

$ ./ dynamic_simulation.py -r sim_16

To visualize the results you can use dynamic_analysis.ipynb Jupyter notebook.

Some precompiled params.json can be found in the params_files folder. Just copy one in the initialized simulation folder, change the name in params.json and run the simulation.

In the src folder two bash files, init_all_sets.sh and init_correlation_test.sh are available to generate some useful standard systems. Just uncomment the rows relative to the system you want to initialize and run the files.

An old version of the program which use spherical coordinates can be found in old_sph_version directory.

• Andrea Maiani ([email protected])