Chapter 8: Q. 8.19 (page 345)
The critical temperature of iron is . Use this value to make a rough estimate of the dipole-dipole interaction energy , in electron-volts.
Short Answer
The dipole interaction energy of iron =
Chapter 8: Q. 8.19 (page 345)
The critical temperature of iron is . Use this value to make a rough estimate of the dipole-dipole interaction energy , in electron-volts.
The dipole interaction energy of iron =
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Get started for freeDraw all the diagrams, connected or disconnected, representing terms in the configuration integral with four factors of . You should find 11 diagrams in total, of which five are connected.
You can estimate the size of any diagram by realizing that is of order 1 out to a distance of about the diameter of a molecule, and beyond that. Hence, a three-dimensional integral of a product of f's will generally give a result that is of the order of the volume of a molecule. Estimate the sizes of all the diagrams shown explicitly in equation and explain why it was necessary to rewrite the series in exponential form.
Consider a gas of "hard spheres," which do not interact at all unless their separation distance is less than , in which case their interaction energy is infinite. Sketch the Mayer -function for this gas, and compute the second virial coefficient. Discuss the result briefly.
Starting from the partition function, calculate the average energy of the one-dimensional Ising model, to verify equation 8.44. Sketch the average energy as a function of temperature.
Modify the ising program to compute the total magnetisation (that is, the sum of all the s values) for each iteration, and to tally how often each possible magnetisation value occurs during a run, plotting the results as a histogram. Run the program for a 5 x 5 lattice at a variety of temperatures, and discuss the results. Sketch a graph of the most likely magnetisation value as a function of temperature. If your computer is fast enough, repeat for a 10 x 10 lattice.
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