Classical and quantum Heisenberg model

[matematikuvol]

In quantum Heisenberg model
$$\hat{H}=-J\sum_{\vec{n},\vec{m}}\hat{\vec{S}}_{\vec{n}}\cdot \hat{\vec{S}}_{\vec{m}}$$
$J$ can be obtained from dispersion experiment. For large spin $S$ even classical Heisenberg model is good for description of Curie temperature for example. Is that with the same $J$ which is obtained from dispersion law? Thanks for the answer! Maybe you know some reference.

 

[matematikuvol]

For example you have spin $S=\frac{7}{2}$ and for example $J=10$ quantum Heisenberg model. And you have Monte Carlo simulation code for classical Heisenberg $S=\infty$. What should you use for $J$ in classical Heisenberg model Monte Carlo code?