Concept explainers
For a two-dimensional Ising model on a square lattice, each dipole (except on the edges) has four “neighbours”—above, below, left, and right. (Diagonal neighbors are normally not included.) What is the total energy (in terms of
Figure 8.4. One particular state of an Ising model on a
Total energy in terms of
Explanation of Solution
Introduction:
Draw a diagram to show one Ising model on
Here, each dipole has four nearest neighboring dipoles except dipoles on edges.
The lattice in above diagram has 14 nearest neighboring dipoles in between parallel dipoles as well as 19 neighboring dipoles in between anti-parallel dipoles in total.
Write the expression of total interaction energy
Simplify the above expression
Conclusion:
Thus, the total energy is
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