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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.pngPhysical Review AAmerican Physical Society (APS)http://www.deepdyve.com/lp/american-physical-society-aps/frustrated-spin-hamiltonians-with-binary-input-vectors-AhBPx7nvFL