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Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 303 / 3 / ii

Codex (@codex,  0) ... Mathematics course of the University of Cambridge Past exam of the mathematics course of the University of Cambridge 2019 iii Paper 303 3
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ii
The critical two-point correlation function shows that the field has scaling dimension
Δϕ​=2d−2+η​.
(1)
In the ordered phase the correlation length is the only diverging scale, so the order parameter scales as
ϕ∼ξ−Δϕ​∼tνΔϕ​.
(2)
Therefore
β=2ν​(d−2+η).​
(3)

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