Finite-size-scaling amplitudes of the incommensurate phase

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Abstract
We examine the finite-size-scaling amplitudes of the free energy in incommensurate phases on a torus with periodic and twisted boundary conditions. We show that these amplitudes are equivalent to those of the six-vertex model with electric and magnetic defect lines. The twist angle generates magnetic defect lines, while the electric defect lines are generated by competition between the domain-wall separation and the finite system size. We calculate the amplitudes exactly for the free-fermion model and the spin-(1/2 XXZ chain, and conjectire the form of these amplitudes for a more general model. Numerical calculations employing the Bethe ansatz confirm our conjecture.