RG flow in coupling space — fixed points, universality & Wilson-Fisher ε-expansion
The Wilson-Fisher fixed point at (u*, r*) controls the Ising universality class in d = 4−ε dimensions. The RG beta functions β_u = −εu + 3u²/(16π²) and β_r = 2r + u determine the flow. Relevant perturbations drive away from criticality (temperature tuning); irrelevant ones decay to zero at the fixed point, producing universality. The critical exponent η = ε²/54 and ν⁻¹ = 2 − ε/3 to O(ε).