The HP model (Dill 1985) is the canonical lattice protein model. Residues are either Hydrophobic (H) or Polar (P). The energy is E = −Σ Jᵢⱼ where the sum is over non-bonded H-H contacts (Jᵢⱼ = 1 for H-H neighbors). The chain is a self-avoiding walk on a 2D square lattice. Monte Carlo explores conformations via pivot moves — a segment is reflected about a random pivot point. The protein folds because hydrophobic residues minimize solvent exposure by forming a buried core.