Disordered
Spin Clusters
A cluster of magnetic
atoms, interacting via short-range exchange forces, will usually
order either ferromagnetically (total spin Stot = Ns),
or antiferromagnetically (total spin Stot = 0). In the
first case, the magnetic moment will be proportional to N, the number
of atoms; in the second case it will be strictly zero.
What happens if the interactions are
chosen randomly, so that some favour ferromagnetism and some favour
antiferromagnetism (as happens in real materials called spin glasses)?
The rules of quantum mechanics tell us that any such system will
have a precise spin quantum number Stot. What values
can this take and now do the results depend on N? We have answered
this question by exact numberical calculations on small clusters,
and find:
Stot can take a range of
values, for different realizations of the disordered bonds.
Averaging our disorder gives an average Stot which scales
as Stot  .
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