** The objective of the test problems in this directory 
   is the following twofold: 
- verify the implementation of the LAMMPS' SPIN package by 
  comparing its results to well-known analytic results, or 
  to simple test problems,
- provide users with simple comparisons, allowing them to 
  better understand what is implemented in the code.

The LAMMPS input file (test-*) can be modified, as well as the
associated python script, in order to try different comparisons.

All scripts can be run by executing the shell script from its
directory. Example:
./run-test-exchange.sh from the validation_damped_exchange/
directory. 

** Below a brief description of the different validation 
   problems:

- validation_damped_precession:
  simulates the damped precession of a single spin in a magnetic
  field. 
  Run as: ./run-test-prec.sh
  Output: x, y and z components of the magnetization, and
  magnetic energy.

- validation_damped_exchange:
  simulates two spins interacting through the exchange
  interaction. The parameters in the LAMMPS input script
  (test-spin-precession.in) are calibrated to match the
  exchange definition in the python script (llg_exchange.py). 
  Run as: ./run-test-exchange.sh
  Output: average magnetization resulting from the damped 
  precession of the two interacting spins. Also plots the 
  evolution of the magnetic energy.
  
- validation_langevin_precession:
  simulates a single spin in a magnetic field and in contact
  with a thermal bath, and compares the statistical averages of 
  the output to the analytical result of the Langevin function. 
  Run as: ./run-test-prec.sh
  Output: statistical average of the z-component of the
  magnetization (along the applied field) and of the magnetic
  energy versus temperature. Comparison to the Langevin function
  results (computed by the python script).
  Note: This example is a reworked version of a test problem 
  provided by Martin Kroger (ETHZ).  
