Abstract
In the. last lecture, we dealt with the ${\rm spin}-{1\over2}$ Ising model, with the Hamiltonian, ${\rm {\cal H}_I = -J \sum\limits_{<ij>}\sigma_i \sigma_j - mH\sum\sigma_i},$ where the coupling between the spins is confined to the z-components, with σ1 = ± 1. We shall now consider a more general Hamiltonian of the form, ${\rm {\cal H}=-{1\over {S^2}} \sum\limits_{<ij>} J_{ij} {\underline S}_i\cdot {\underline S}_j -{m\over S}\sum\limits_{i=1}^N {\underline S}_i\cdot{\underline H}_i}.$ The spins ${\rm {\underline S}_i}$ are now D-dimensional vectors given by, ${\rm {\underline S}_i= \{S_i^1\ S_i^2\ \cdot\cdot\cdot\ S_i^D\}}$ The interaction between the spins takes the form of a scalar product ${\rm {\underline S}_i\cdot}{\rm {\underline S}_j}$ and (2) defines the D-vector model.
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© 1982 Plenum Press, New York
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McKenzie, S. (1982). Series Expansions for the Classical Vector Model. In: Lévy, M., Le Guillou, JC., Zinn-Justin, J. (eds) Phase Transitions Cargèse 1980. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3347-0_11
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DOI: https://doi.org/10.1007/978-1-4613-3347-0_11
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