Abstract: The response to the temperature for a two-Dimensional (2D) spin array of a lattice of 2×2 size Ising-Onsager type was compared with the exact solution and simulation in the formalism of the Monte Carlo simulation. The functions energy, magnetization, heat capacity and susceptibility per spin determined by Monte Carlo simulation and the Metropolis algorithm, showed dispersion of close to 1% when compared to the exact solution and the Onsager model. The finite scaling method for 2D lattices of 2×2, 4×4, 8×8, 16×16, 32×32 and 64×64 size, allowed the calculation of the critical exponents of scaling function magnetization, specific heat capacity and susceptibility. The results show that the scaling functions are independent of lattice size but dependent on temperature and the critical exponent (class of universality).