The free energy singularity of the asymmetric six-vertex model and the excitations of the asymmetric XXZ chain Original Research Article

We consider the asymmetric six-vertex model, widely used to describe the equilibrium shape of crystals, and the relevant asymmetric XXZ chain. By means of the Bethe-ansatz solution we determine the free energy singularity, as function of the external field, at two special points on the phase boundary. We confirm the exponent 32 (checked experimentally, as the antiferroelectric ordered phase is reached from the incommensurate phase normally to this boundary, and we determine a new singularity along the tangential direction. Both singularities describe the rounding off of the crystal near a facet. At this point the hole excitations of the spin chain show dispersion relations ΔE ∼ (ΔP)12 at small momenta, leading to a finite-size scaling ΔE ∼ N−12 for the low-lying excited states, N being the chain size. We discuss the nature of the phase transition and the behavior of arrow-arrow correlation lengths in the ordered phase.