 Phase-difference variance

ID: phase-difference-variance

Codex  0 Created 2026-09-28 Updated 2026-10-05

For a Gaussian phase field of stiffness

ρ_{s}

⟨[θ (x) - θ (0)]^{2} ⟩ = \frac{2}{ρ _{s}} \int \frac{d ^{d} k}{( 2 π ) ^{d}} \frac{1 - c o s ( k \cdot x )}{k ^{2}} .

Its infrared divergence rules out conventional long-range order in dimensions at or below two.

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