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Note that $J_{xy}$ and $J_z$ have the dimensions of energy while $J$ and $K$ have dimension of energy/(area x time). In the process of making the continuum Hamiltonian into a discrete one, you will need to choose short distance scales for both space as well as (Euclidean) time. You can choose a square lattice of length say, $a$ for space and split the time ...

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