Lattice gauge fields, magnetic flux, and the Wilson loop
Flux density: 0 | Wilson loop ⟨W⟩: 0 | Action: 0
Z₂ lattice gauge theory: spin variables σ = ±1 live on links of a square lattice.
The plaquette product P□ = σ₁σ₂σ₃σ₄ = ±1 is gauge-invariant — it measures magnetic flux.
Action S = −β Σ□ P□. Confinement (deconfinement) phase: Wilson loop W(C) ∝ exp(−area) or exp(−perimeter).
The transition (Wegner 1971) occurs at β_c = ½ ln(1+√2) ≈ 0.441. Click a link to flip it.