Quantum Phase Diagram — Transverse-Field Ising Chain

H = -J Σ σᵢᶻσᵢ₊₁ᶻ - h Σ σᵢˣ. Exact solution via Jordan-Wigner fermions. Quantum phase transition at h/J=1: ferromagnetic (h<J) vs. paramagnetic (h>J). Critical exponents: ν=1, z=1 (CFT c=1/2).

Parameters

J (Ising coupling): 1.00 h (transverse field): 1.50 Chain length N: 40

PARAMAGNETIC

h/J = —
Gap Δ = —
⟨σᶻ⟩ = —
ξ ∝ |h/J−1|^{-ν}
c = 1/2 at QCP