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Frustrated spin Hamiltonians with binary input vectors

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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