Phase transitions

Qualitative change with a tuning parameter — first-order vs continuous, critical points, and quantum criticality.

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.
• The Mott Transition in DMFT: Phase Diagram and V₂O₃ Mott Physics in Correlated Lattices Running the DMFT+IPT loop on the Bethe lattice traces the interaction-driven Mott transition — the three-peak spectral structure, the Fermi-liquid self-energy, the coexistence region with critical interactions U_c1 ≈ 2.54 and U_c2 ≈ 3.27, and a (U,T) phase diagram whose first-order line and critical endpoint reproduce the paramagnetic metal–insulator transition of V₂O₃.