(a) Write down the partition function for a 1-dimensional Ising lattice as a sum over terms describing all possible spin organizations.

(b) Show that by separating into even and odd numbered spins, it is possible to factor the partition function and relate z(N, K)exactly to z(N/2, K'). Specifically, show that

where K' = ln[cosh(2K)]/2, and f (K) = 2[cosh(2K)]^1/2.

(c) Use these relations to demonstrate that the 1-dimensional Ising lattice does not exhibit a second-order phase transition.

Transcribed Image Text:

z(N, K) = f(K)N/²z(N/2, K') (5.94)