Direction dependent free energy singularity of the asymmetric six-vertex model

The transition from the ordered commensurate phase to the incommensurate gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields $(h,v)$. In the $(h,v)$ plane, the phase boundary is approached along straight lines $\delta v=k \delta h$, where $(\delta h,\delta v)$ measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski-Talapov transition $\delta f \sim const (\delta h)^{3/2}$ for any direction other than the tangential one. In the latter case $\delta f$ shows a discontinuity in the third derivative.