For an antiferromagnetic spin-1/2 ring with an odd number of sites, the spontaneous magnetization decays algebraically to zero and is ferromagnetic-looking, so boundary conditions can destroy local order.
To overcome this problem, we proceed as in Ref
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The Frustration of being Odd: How Boundary Conditions can destroy Local Order
For an antiferromagnetic spin-1/2 ring with an odd number of sites, the spontaneous magnetization decays algebraically to zero and is ferromagnetic-looking, so boundary conditions can destroy local order.