Communications in Mathematical Physics

, Volume 199, Issue 3, pp 493–520 | Cite as

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

  • Tadeusz Balaban
  • Michael O'Carroll


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.


Correlation Function Temperature Property Spin Model Goldstone Boson Temperature Lattice 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Tadeusz Balaban
    • 1
  • Michael O'Carroll
    • 2
  1. 1.Mathematics Department, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USAUS
  2. 2.Departamento de Física do ICEX, Universidade Federal de Minas Gerais, Belo Horizonte, MG, BrasilBR

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