Application of the $O(N)$-Hyperspherical Harmonics to the Study of the Continuum Limits of One-Dimensional $σ$-Models and to the Generation of High-Temperature Expansions in Higher Dimensions

Details Application of the $O(N)$-Hyperspherical Harmonics to the Study of the Continuum Limits of One-Dimensional $σ$-Models and to the Generation of High-Temperature Expansions in Higher Dimensions Application of the $O(N)$-Hyperspherical Harmonics to the Study of the Continuum Limits of One-Dimensional $σ$-Models and to the Generation of High-Temperature Expansions in Higher Dimensions

1995-09-12

arxiv.org/abs/hep-lat/9509034v1

Nucl.Phys.Proc.Suppl. 47 (1996) 759-762

Physics

High Energy Physics

High Energy Physics - Lattice

59208 bytes uuencoded gzip'ed (expands to 135067 bytes Postscript); 4 pages including all figures; contribution to Lattice '95

Scientific paper

10.1016/0920-5632(96)00168-5

In this talk we present the exact solution of the most general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbour interactions, and we discuss the possible continuum limits. All these results are obtained using a high-temperature expansion in terms of hyperspherical harmonics. Applications in higher dimensions of the same technique are then discussed.

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