3D Transverse-Field Ising — Quantum Critical Point
Wilson-Fisher fixed point, divergent correlation length, anomalous scaling
--
ξ / a
--
⟨σ^z⟩
--
Gap Δ / J
0.036
η (anomalous dim)
0.630
ν (corr. length exp)
H = −J Σ σ^z_i σ^z_j − g Σ σ^x_i has a QCP at g_c ≈ 3.044J in 3D (Wilson-Fisher universality class, same as 3D classical Ising). Critical exponents: ν ≈ 0.630 (correlation length ξ ~ |g−g_c|^{−ν}), β ≈ 0.326 (order ⟨σ^z⟩ ~ (g_c−g)^β), η ≈ 0.036 (anomalous dimension, G(r) ~ r^{−(d−2+η)}). The quantum-to-classical mapping: d-dim quantum = (d+z)-dim classical with z=1 for this universality class.