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For the 2D Ising model, we analyzed dependences of thermodynamiccharacteristics on number of spins by means of computer simulations. Wecompared experimental data obtained using the Fisher-Kasteleyn algorithm on asquare lattice with $N=l{\times}l$ spins and the asymptotic Onsager solution($N\to\infty$). We derived empirical expressions for critical parameters asfunctions of $N$ and generalized the Onsager solution on the case of afinite-size lattice. Our analytical expressions for the free energy and itsderivatives (the internal energy, the energy dispersion and the heat capacity)describe accurately the results of computer simulations. We showed that when$N$ increased the heat capacity in the critical point increased as $lnN$. Wespecified restrictions on the accuracy of the critical temperature due tofinite size of our system. Also in the finite-dimensional case, we obtainedexpressions describing temperature dependences of the magnetization and thecorrelation length. They are in a good qualitative agreement with the resultsof computer simulations by means of the dynamic Metropolis Monte Carlo method.

Dependence of critical parameters of 2D Ising model on lattice size