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m Reference correction. Onsager did not know or use the connection to fermionic field theory. |
m →Lattice gas: +. |
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So the energy of the lattice gas is:
<math display="block">E = - \frac{1}{2} \sum_{\langle i,j \rangle} 4 J B_i B_j + \sum_i \mu B_i.</math>
Rewriting the bits in terms of spins, <math>B_i = (S_i + 1)/2. </math>
<math display="block">E = - \frac{1}{2} \sum_{\langle i,j \rangle} J S_i S_j - \frac{1}{2} \sum_i (4 J - \mu) S_i.</math>
For lattices where every site has an equal number of neighbors, this is the Ising model with a magnetic field ''h'' = (''zJ'' − ''μ'')/2, where ''z'' is the number of neighbors.
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