An Introduction to Thermal Physics
An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 8.2, Problem 15P

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 ε ) for the particular state of the 4 × 4 square lattice shown in Figure 8.4?

Chapter 8.2, Problem 15P, For a two-dimensional Ising model on a square lattice, each dipole (except on the edges) has four

Figure 8.4. One particular state of an Ising model on a 4 × 4 square lattice (Problem 8.15).

Expert Solution & Answer
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To determine

Total energy in terms of ε .

Explanation of Solution

Introduction:

Draw a diagram to show one Ising model on (4×4) lattice

  An Introduction to Thermal Physics, Chapter 8.2, Problem 15P

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 U of the lattice

  U=(10)(ε)+(14)(ε)

Simplify the above expression

  U=4ε

Conclusion:

Thus, the total energy is 4ε in terms of ε .

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Ising model | A Bird's Eye View | Solid State Physics; Author: Pretty Much Physics;https://www.youtube.com/watch?v=1CCZkHPrhzk;License: Standard YouTube License, CC-BY