Lattice Gauge Theory: U(1) Plaquette Monte Carlo

This simulator builds a real 2D compact U(1) lattice gauge theory from scratch: a periodic grid of sites carries phase variables on every link, the elementary gauge-invariant observable is the plaquette loop, and a Metropolis Monte Carlo sampler thermalizes the plaquette action S = β Σ(1 − cos θ_p) sweep by sweep. Links are colored by their phase and plaquettes by their local flux, so you can watch the lattice cool into an ordered, low-flux configuration at large β or boil into a disordered one at small β. A live Wilson loop — the same gauge-invariant probe used in real lattice QCD to diagnose quark confinement — is traced around a highlighted rectangle on the lattice, and its value falls off with loop area exactly as the area law predicts, the signature of confinement.