About
In φ⁴ theory, two couplings matter near d=4: the mass r (tuning to criticality) and the quartic interaction u. Wilson's RG integrates out a thin momentum shell near Λ, giving flow equations:
dr/dl = 2r + a·u − b·u·r
du/dl = ε·u − c·u²
where ε=4−d. Fixed points determine universality classes. The Wilson-Fisher fixed point at u*>0 governs the 3D Ising class.
Controls
Fixed Points
Gaussian (u=0,r=0)
Wilson-Fisher
Ordered phase
Arrows show RG flow direction (increasing RG scale l). The critical manifold separates phases.