Logarithmic corrections to finite-size scaling in the four-state Potts model

The leading corrections to finite-size scaling predictions for eigenvalues of the quantum Hamiltonian limit of the critical four-state Potts model are calculated analytically from the Bethe ansatz equations for equivalent eigenstates of a modified XXZ chain. Scaled gaps are found to behave for large chain length L as x+d{Plimsoll sign}L+0[(ln L)^-1], where x is the anomalous dimension of the associated primary scaling operator. For the gaps associated with the energy and magnetic operators, the values of the amplitudes d are in agreement with predictions of conformai invariance. The implications of these analytical results for the extrapolation of finite lattice data are discussed. Accurate estimates of x and d are found to be extremely difficult even with data available from large lattices, L∼500.