Calculate Quantum Partition Function

[QFT25]

Homework Statement

Consider the case when the three Ising spins are replaced by quantum spins 1/2's with a Hamiltonian

H=-J(s1.s2+s2.s3+s3.s1) calcualte the quantum partition function

Homework Equations

Partition function is the sum of E^(-H*B) where B is 1/kt

The Attempt at a Solution

Because this is the discrete case I'm assuming the fact that this is a quantum partition function doesn't make much of a difference. there are eight possibility, two of them are (1/2,1/2,1/2),(1/2,1/2,-1/2) and when I sum them all up I get 2*E^(3*J*B/4)+6*E^(-J*B/4). Is my approach correct or am I missing something subtle because this is quantum partition function?

 

[TSny]

Your approach and result look correct to me.