Critical coefficients

We derive exact analytical expressions for the numerical coefficients $A_\psi$, $A_{gap}$ in the scaling laws for the fermion condensate $<\bar \psi \psi> = A_\psi m^{1/3} g^{2/3}$ and for the mass of the lightest state $\mu_{gap} = A_{gap} m^{2/3} g^{1/3}$ in the Schwinger model with two light flavors, $m \ll g$. $A_\psi$ and $A_{gap}$ are expressed via certain ratios of $\Gamma$--functions. Numerically, $A_\psi = -0.244\ldots, A_{gap} = 1.593\ldots$ . The same is done for the standard square lattice Ising model at $T = T_c$. Using recent Fateev's results, we get $<\sigma_{lat}> = 1.058\ldots (H_{lat}/T_c)^{1/15}$ for the magnetization and $M_{gap} = a/\xi = 4.010\ldots (H_{lat}/T_c)^{8/15}$ for the inverse correlation length ($a$ is the lattice spacing). The theoretical prediction for $<\sigma^{lat}>$ is in a perfect agreement with available numerical data. However, the theoretical result for $M_{gap}$ is $\sim \sqrt{2}$ larger than what is seen in experiment. The reasons of disagreement are currently not clear.