We investigate the effect of the marginal operator on the critical exponents of the one-dimensional S=1/2 Heisenberg model, using the relation between the critical exponents and the energy gaps of the finite system. The energy gaps behave as ΔE1/L with the logarithmic corrections from the marginally irrelevant operator. The numerical results obtained with the Bethe ansatz are well explained by the two-loop renormalization of the marginal coupling. Thus the discrepancies between the one-loop renormalization prediction and numerical results are resolved, though it is found that the nonuniversal constant of the logarithmic correction in the ground state does not agree with the asymptotic expansion of the Bethe ansatz.
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