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.
End of preview. The entire article is 7 pages. Rent for Free