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, left-angle bar ψψ right-angle=-0.388 hor-ellipsis m1/3g2/3, Mgap=2.008 hor-ellipsis m2/3g1/3. The same is done for the standard square lattice Ising model at T=Tc. We get left-angle σlat right-angle=1.058 hor-ellipsis hlat1/15 for the magnetization and Mgap=1/ξ=4.010 hor-ellipsis hlat8/15 for the inverse correlation length. The theoretical prediction for left-angle σlat right-angle is in perfect agreement with numerical data. Two available numerical papers give the values of Mgap which differ from each other by a factor ∼√(2). The theoretical result agrees with one of them. copyright 1997 The American Physical Society