Universality Classes

Why systems with different microscopic physics share identical critical exponents

Select Class

Universality Classes

Classβγνη

Key Insight

Only: d, symmetry, range of interactions matter
The RG fixed point determines universality. Near Tc, details wash out — only symmetry and dimension survive. A magnet and a liquid-gas system can be in the same universality class.
H ~ ∫[(∇φ)² + rφ² + uφ&sup4;]
All Ising-like systems (Z2 symmetry, scalar order param, d=3) share exponents regardless of lattice structure or interaction strength.