Exact universal amplitude ratios for two-dimensional Ising models and a quantum spin chain

Let f(N) and xi (-1)(N) represent, respectively, the free energy per spin a nd the inverse spin-spin correlation length of the critical Ising model on a N X infinity lattice, with f(N) --> f(x) as N --> infinity. We obtain ana lytic expressions for ak and br, in the expansions N(f(N) - f(infinity)) = Sigma (infinity)(k=1) a(k)/N2k-1 and xi (-1)(N) = Sigma (infinity)(k=1) b(k )/N2k-1 for square, honeycomb, and plane-triangular lattices, and find that b(k)/a(k) = (2(2k) - 1)/(2(2k-1) - 1) for all of these lattices, i.e., the amplitude ratio b(k)/a(k) is universal. We also obtain similar results for a critical quantum spin chain and find that such results could be understo od from a perturbated conformal field theory.