Quantum Phase Transition: Transverse-Field Ising Model

H = −J Σ σᵢᶻσᵢ₊₁ᶻ − h Σ σᵢˣ. The gap closes at h/J = 1, marking a quantum critical point between ordered (ferromagnetic) and disordered phases.

Field h/J: 0.50

Chain length N: 20

Temperature kT/J: 0.10

Phase: Ordered | Gap Δ = — | ⟨σᶻ⟩ = —