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 y_{i}
interact with each other, transform to new variables,
w_{i} = y_{i}  y_{i1}
The constraint on the endpoints then becomes
If you now write the Hamiltonian in terms of the w_{i}, the partition function would factor
into a product of independent pieces, if it were not for the above
constraint on the sum of the w_{i}.
If you can't figure out how to handle the constraint, here
is another hint.
(The above transformation works well for part (b) also.)
