Low Temperature Properties for Correlation Functions in Classical N-Vector Spin Models

Abstract:

We obtain convergent multi-scale expansions for the one-and two-point correlation functions of the low temperature lattice classical N– vector spin model in d≥ 3 dimensions, N≥ 2. The Gibbs factor is taken as

where , , , are large and 0 < v≤ 1. In the thermodynamic and limits, with h=e ₁, and Δ≡∂^★∂, the expansion gives (spontaneous magnetization), , (Goldstone Bosons), , and , where , for some ρ > 0, and c ₀ is aprecisely determined constant.