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Springer eBooks

The Spin Operator and Spin Functions

Ruben Pauncz

Published Jan 1, 2000• 0 citations
Publisher
DOI
10.1007/978-1-4615-4291-9_1

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The authors derive a functional integral representation for the partition function of the transverse Ising model. The spin operators are replaced by fermion operators and special care is taken to achieve complete equivalence of the spin model and the fermion model. They discuss several approximations for the functional integral and show that in a recent paper on spin glasses, where a similar method was used, the original spin model and the fermion model, which was obtained by replacing the spin operators by fermion operators, are not equivalent and have different critical temperatures.
We construct polarized spin reversal operator (PSRO) which yields a class of representations for the BCN type of Weyl algebra, and subsequently use this PSRO to find out novel exactly solvable variants of the BCN type of spin Calogero model. The strong coupling limit of such spin Calogero models generates the BCN type of Polychronakos spin chains with PSRO. We derive the exact spectra of the BCN type of spin Calogero models with PSRO and compute the partition functions of the related spin chains by using the freezing trick. We also find out an interesting relation between the partition functions of the BCN type and AN−1 type of Polychronakos spin chains. Finally, we study spectral properties like level density and distribution of spacing between consecutive energy levels for BCN type of Polychronakos spin chains with PSRO.