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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

Massimo Campostrini·Attilio Cucchieri·Tereza Mendes·Andrea Pelissetto·Paolo Rossi·Alan D. Sokal·Ettore Vicari
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Abstract

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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Massimo Campostrini, Attilio Cucchieri, Tereza Mendes, Andrea Pelissetto, Paolo Rossi, Alan D. Sokal, Ettore Vicari. 1995-09-12. 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. https://doi.org/10.1016/0920-5632(96)00168-5

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