q-Hypergeometric Series and Macdonald Functions

We derive a duality formula for two-row Macdonald functions by studying their relation with basic hypergeometric functions. We introduce two parameter vertex operators to construct a family of symmetric functions generalizing Hall-Littlewood functions. Their relation with Macdonald functions is governed by a very well-poised q-hypergeometric functions of type ₄₃, for which we obtain linear transformation formulas in terms of the Jacobi theta function and the q-Gamma function. The transformation formulas are then used to give the duality formula and a new formula for two-row Macdonald functions in terms of the vertex operators. The Jack polynomials are also treated accordingly.     

Local spin correlations in partially frustrated amorphous Fe-Mn

Mössbauer measurements in a-(Fe_0.765Mn_0.235)₇₈Sn₂Si₆B₁₄ have been performed with⁵⁷Fe and¹¹⁹Sn. Both hyperfine fields show a kink near 70 K, indicating a freezing of the transverse spins. The ratio of the two hyperfine fields contains information about the correlation of the transverse spins. The ratioB _hf(Sn)/B _hf(Fe) stays constant aboveT _xy and rises belowT _xy . This indicates an alignment of the transverse spins on a local scale, as was also found inAuFe and a-FeZr.