1D lattice gauge theory · Wilson action · Metropolis Monte Carlo · confinement–deconfinement
Plaquette vs β
S = -β Σ Re(U_p)
U_p = U₁·U₂·U₃†·U₄†
β small → confined (U_p→0)
β large → free (U_p→1)
1D: exact result P(U)∝e^{βcos(θ)}
Polyakov Loop & String Tension
⟨L⟩ = —
String tension σ ≈ —
V(r) = σr + ... (confinement)
Polyakov loop L = Tr(∏ U_t)
⟨L⟩=0 → confined
⟨L⟩≠0 → deconfined