### 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.

### 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: $(\langle M^2\rangle-\langle M\rangle^2)/k_B/T$.