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

TY - JOUR

T1 - Low temperature properties for correlation functions in classical N-vector spin models

AU - Balaban, Tadeusz

AU - O'Carroll, Michael

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0033249580

UR - https://www.scopus.com/pages/publications/0033249580#tab=citedBy

U2 - 10.1007/s002200050510

DO - 10.1007/s002200050510

M3 - Article

SN - 0010-3616

VL - 199

SP - 493

EP - 520

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 3

ER -