The free energy singularity of the asymmetric sixvertex model and the excitations of the asymmetric XXZ chain
Abstract
We consider the asymmetric sixvertex model, widely used to describe the equilibrium shape of crystals, and the relevant asymmetric XXZ chain. By means of the Betheansatz 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 {3}/{2} (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) ^{{1}/{2}} at small momenta, leading to a finitesize scaling ΔE ∼ N ^{}{1}/{2} for the lowlying excited states, N being the chain size. We discuss the nature of the phase transition and the behavior of arrowarrow correlation lengths in the ordered phase.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(97)000783
 arXiv:
 arXiv:condmat/9606137
 Bibcode:
 1997NuPhB.493..541A
 Keywords:

 Condensed Matter;
 High Energy Physics  Theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 42 pages, LaTeX, 3 psfigures uuencoded