Thermal field

$$\mathbf{H}_\mathrm{th}= \eta \sqrt{ 2 \frac{\alpha}{1+\a... ...frac{k_B T}{\mu_0 \gamma' \Delta x^3 M_\mathrm{s} \Delta t} }$$

$\eta$	1	standard Gaussian process with mean zero and variance 1
$\alpha$		damping constant,
$k_B$	(J/K)	Boltzmann's constant,
$T$	(K)	Temperature,
$\gamma'$	(1/Ts)	gyromagnetic ratio (),
$\Delta x^3$	(m$^3$)	discretization volume
$\Delta t$	(s)	step size of time integration

Then, the equation of motion () is integrated for each computational cell for a certain discrete time step. Since the magnetization distribution has changed, the effective field is calculated again, before the next time integration step is performed.