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

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.

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

Cited by in corpus (2)

• A strong-coupling analysis of two-dimensional O(N) sigma models with N<=2 on square, triangular and honeycomb lattices
• Continuum Limits and Exact Finite-Size-Scaling Functions for One-Dimensional $O(N)$-Invariant Spin Models