4.5. Self-duality Consider the function Z(K) = K1/4 n= eKn2 that satisfies Z(K) = Z 1 K . a. Show that in

4.5. Self-duality Consider the function Z(K) = K1/4

∞



n=−∞

e−πKn2 that satisfies Z(K) = Z  1 K .

a. Show that in this case the duality relation does not imply a phase transition at K = 1.

b. How many terms are necessary in the original expression to compute Z(K) with a precision 10−4 for K = 0.01? How many terms are needed to reach the same precision by using its dual expression?