Scaling & universality

Why microscopically different systems share critical behaviour — relevant couplings, exponents, and fixed points.

Every topic that illustrates this idea, drawn from across all subjects.

• Weak Coupling: Mean-Field Theory and the Slater Insulator Mott Physics in Correlated Lattices Starting from the non-interacting limit, a mean-field decoupling of the Hubbard interaction with staggered magnetization gives an antiferromagnetic two-band insulator. Solving the self-consistent gap equation reveals a Slater gap that opens exponentially at weak coupling and crosses over to the Mott gap Δ → U/2 at strong coupling.