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Frustrated spin Hamiltonians with binary input vectors

Structures of composite spin operators are analyzed which appear in models of neural networks of the type which Amit et al . have recently investigated. A binary basis of size N = 2 M is introduced to study a problem of N quantum-mechanical spin operators. The Z ( 2 ) M group structure of the binary basis allows for many decompositions of the SU(2) N spin algebra. These become useful in studying and solving generalized frustrated Heisenberg as well as Ising models. Using these techniques for quantum-mechanical generalized spin operators, we derive an explicit representation of the partition function of classical statistical-mechanics models, in terms of a series summation over components of collective spin variables. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

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