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PHY 418: Statistical Mechanics I
Prof. S. Teitel stte@pas.rochester.edu ---- Spring 2018

Problem Set 4 Hint 1

To deal with the fact that the variables yi interact with each other, transform to new variables,

wi = yi - yi-1

The constraint on the endpoints then becomes


wi = Y

If you now write the Hamiltonian in terms of the wi, the partition function would factor into a product of independent pieces, if it were not for the above constraint on the sum of the wi.

If you can't figure out how to handle the constraint, here is another hint.

(The above transformation works well for part (b) also.)