Critical amplitudes in two-dimensional theories

Using recent thermodynamic Bethe ansatz results, we derive exact analytical expressions for the critical amplitudes in the scaling laws for the fermion condensate and for the mass gap in the Schwinger model with two light flavors. Numerically, [<(Psi)over bar>,Psi] = -0.388... m(1/3)g(2/3), M(gap)= 2.008... m(2/3)g(1/3). The same is done for the standard square lattice Ising model at T = T-c. We get (sigma(lat)) = 1.058...h(lat)(1/15) for the magnetization and M(gap)= 1/xi = 4.010... h(lat)(8/15) for the inverse correlation length. The theoretical prediction for [sigma(lat)] is in perfect agreement with numerical data. Two available numerical papers give the values of M(gap) which differ from each other by a factor approximate to root 2. The theoretical result agrees with one of them.