Low temperature properties for correlation functions in classical N-vector spin models

Tadeusz Balaban, Michael O'Carroll

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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 exp[-β(1/2||∂||2 + λ/8|||2 - 1||2 + v/2|| - h||2)], where (x), h ∈ RN, x ∈ Zd, \h\ = 1, β < ∞, λ ≥ ∞ are large and 0 < v ≤ 1. In the thermodynamic and v ↓ 0 limits, with h = e1, and Δ ≡ ∂* ∂, the expansion gives 〈1(x)〉 = 1+0(1/β1/2) (spontaneous magnetization), 〈1(x)i(y)〉 =0, 〈i(x)i(y)〉 = c0Δ-1(x,y) + R(x, y) (Goldstone Bosons), i = 2,3, ... , N, and 〈1(x)1(y)〉T = R′(x, y), where |R(x, y)|, |R′(x, y)| < 0(1)(1 + |x - y|)d-2+ρ for some ρ > 0, and C0 is aprecisely determined constant.

Original languageEnglish (US)
Pages (from-to)493-520
Number of pages28
JournalCommunications In Mathematical Physics
Volume199
Issue number3
DOIs
StatePublished - 1999

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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