PHY 418: Statistical Mechanics I
Prof. S. Teitel firstname.lastname@example.org ---- 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
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.)