Z₂ Lattice Gauge Theory

2D square lattice with Z₂ link variables ±1. Monte Carlo simulation shows confinement vs deconfinement.

Parameters

Confined
β_c ≈ 0.44 (Z₂ in 2D)
Plaquette ⟨P⟩: 0.00
Energy/link: 0.00
Accepted: 0%
Sweep: 0
Z₂ lattice gauge theory has action S = −β Σ_{plaquettes} P, where P = U₁U₂U₃U₄ ∈ {±1} is the product of links around each plaquette. Confinement: At low β (high T), ⟨W(C)⟩ ~ e^{−σ·Area} — Wilson loop decays with area law → quarks are confined. Deconfinement: At high β (low T), ⟨W(C)⟩ ~ e^{−α·Perimeter} — perimeter law → free charges. Phase transition: β_c ≈ 0.44 in 2D Z₂ (dual to 2D Ising model). Click links to manually flip them. Colors: yellow=+1, blue=−1.