2D U(1) lattice gauge theory — Wilson action, Monte Carlo thermalization
Average Plaquette ⟨P⟩
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Plaquette Action S/N
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MC Sweeps
0
Acceptance Rate
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Color: hue = link angle θ ∈ [−π, π] Brightness: plaquette action contribution Wilson loop: click to measure
In lattice gauge theory, U(1) link variables Uμ(x) = eiθ live on lattice edges.
The Wilson plaquette action is S = β·Σ(1 − cos(θ□)) where θ□
is the sum of link angles around each elementary square. Monte Carlo updates sample the path integral via
Metropolis algorithm. At large β (weak coupling) the lattice is ordered; at small β (strong coupling)
it disorders — analogous to confinement in QCD.