Gauge Field Wilson Loop — Lattice Gauge Theory

U(1) lattice gauge theory · plaquette action · confinement visualization

Coupling β (inverse g²) 1.50

Temperature (Monte Carlo) 1.00

Loop Size 2

Observables

Average Plaquette ⟨P⟩—

Wilson Loop W(R,T)—

String Tension σ—

Confinement Phase—

Wilson loop W(C) = Tr[∏U_μ] is the order parameter for confinement. For small β (strong coupling): W∝exp(−σ·Area) — area law → confinement. For large β (weak coupling): W∝exp(−perimeter) — deconfined phase. Click lattice to place a Wilson loop. Colors show link phases θ∈[−π,π].