(sw-fstat)=

# sw_fstat

## Syntax
  
`parOut = sw_fstat(state, parIn, T, E, M, nExt)`
  
## Description
  
`parOut = sw_fstat(state, parIn, T, E, M, nExt)` calculates statistical
properties of different physical variables over several sampled state.
The function is called by [spinw.anneal](#spinw-anneal).
  
## Input Arguments
  
`state`
: Defines the task of the function.
  * `1`   Initialize the parOut structure.
  * `2`   Store the parameters of the physical state.
  * `3`   Calculate physical properties from the variable
          statistics.
  
`parIn`
: Same as `parOut`.
  
`T`
: Temperature of the system, row vector with $n_T$ number of elements.
  
`E`
: Energy of the system, row vector with $n_T$ number of elements.
  
`M`
: Magnetic moment of every atom in a matrix with dimensions of $[d_{spin}\times n_{magExt}\cdot n_T]$.
  
`nExt`
: Size of the magnetic supercell, column vector of 3 integers.
  
`kB`
: Boltzmann constant, units of temperature.
  
## Output Arguments
  
`parOut`
: Output parameter structure with the following fields:
  * `nStat`   The number of evaluated states.
  * `M`       $\langle M\rangle$ averaged over all magnetic moment stored
              in a matrix with dimensions of $[d){spin}\times
              n_{magExt}\cdot n_T]$.
  * `M2`      $\langle M^2\rangle$ averaged over all magnetic moment
              stored in a matrix with dimensions of $[d){spin}\times
              n_{magExt}\cdot n_T]$.
  * `E`       $\langle E\rangle$  summed over all magnetic moment.
  * `E2`      $\langle E^2\rangle$  summed over all magnetic moment.
 
For the final execution, the following parameters are calculated:
`parOut`
: Array of struct with $n_T$ number of elements:
  * `avgM`    Average components of the magnetisation over $n_{stat}$ runs,
              matrix with dimensions of $[3\times n_{magExt}]$.
  * `stdM`    Standard deviation of the mgnetisation components over
              $n_{stat}$ runs, matrix with dimensions of $[3\times n_{magExt}]$.
  * `avgE`    Average system energy per spin over $n_{stat}$ runs, scalar.
  * `stdE`    Standard deviation of the system energy per spin over
              $n_{stat}$ runs, scalar.
  * `T`       Final temperature of the sample.
  * `Cp`      Heat capacity of the sample: $(\langle E^2\rangle-\langle E\rangle^2)/k_B/T^2$.
  * `Chi`     Magnetic susceptibility of the sample: $(\langle M^2\rangle-\langle M\rangle^2)/k_B/T$.
  
## See Also
  
[spinw.anneal](#spinw-anneal)