Critical behavior of the two-dimensional order-disorder phase transition of the (2×2)-2H structure on Ni(111) was studied by high-resolution low-energy electron-diffraction experiments, both for the pure system and with atomic oxygen, at concentrations between 0.3% and 3% of a monolayer added as an impurity. By quantitative profile analysis of several superstructure spots as a function of temperature the critical exponents, and were determined over a range in the reduced temperature, t=(T-Tc)/Tc, between 0.001 and 0.1. At smaller values of t the system is finite-size limited. Crossover between four-state Potts behavior further away from Tc and exponents close to those of the two-dimensional Ising class were found. The crossover temperature depends systematically on the concentration of oxygen. We conclude that oxygen atoms seem to act like quenched impurities on this surface, similar to local defects already present at concentrations of 10-3 of a monolayer on the clean surface. © 1995 The American Physical Society.