I don't understand this idea. For example we have cubic crystal which has a lot of unit cells. We define spin variable of center of cell like [tex]S_c[/tex]. And spin variable of nearest neighbour cells with [tex]S_{c+r}[/tex]. So the cell hamiltonian is(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\hat{H}=\frac{1}{2}J\sum_{c}\sum_{r}(S_c-S_{c+r})^2+\sum_cU(S_c^2)[/tex]

This model is simulation of uniaxial feromagnet.

I have three question:

1. What's the difference between Ising model and 1d Heisenberg model?

2. Why this model is better than Ising model with no cells? Where we have just spins which interract.

[tex]\hat{H}=-J\sum_iS_{i}S_{i+1}[/tex]

3. What [tex]\sum_cU(S_c^2)[/tex] means physically?

Tnx.

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# Ising cell hamiltonian

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