Why Is Entropy Non-Zero in This Hamiltonian System?

[romeo31415]

Homework Statement

Bonjour,

Given the hamiltonian

Show that

The Attempt at a Solution

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I cannot explain why S=0

 

[MisterX]

One thing you may be able do for is use the exact solution for the partition function $Z$ of the Ising chain.
$S = \partial_T k_B T \ln Z$

In other situations like this one may be able to start by using $S = k_B \ln \Omega(T, H)$, where $\Omega(T, H)$ is the number of states corresponding to T and H.