q-state Potts model: H = −J Σ_{⟨ij⟩} δ(sᵢ,sⱼ). Heat-bath update: P(sᵢ=k) ∝ exp(βJ·n_k) where n_k is the number of neighbors in state k. Critical temperature: T_c = J/ln(1+√q). Phase transition: for q≤4 the transition is second-order (continuous); for q>4 it is first-order, with a discontinuous jump in M and latent heat. The specific heat C_V peaks sharply at T_c. Colors represent the q distinct spin states.