Renormalization Group — φ⁴ Wilson & ε-Expansion

RG flow in coupling constant space for φ⁴ theory. Wilson-Fisher fixed point emerges below d=4. ε=4−d expansion reveals critical exponents.

RG Parameters

ε = 1.0 | η = — | ν = —
Wilson-Fisher fixed point (1972): at ε=4−d order, the RG β-functions have a non-trivial fixed point u* = ε(N+8)/(N+8)·(16π²/3) [schematic]. Critical exponents to O(ε):
η = (N+2)ε²/[2(N+8)²]
ν = ½ + (N+2)ε/[4(N+8)]

Click canvas to launch RG trajectory from that point. Green dot = Wilson-Fisher FP.