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

Abstract

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 $δv=k δh$, where $(δh,δv)$ 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 $δf \sim const (δh)^{3/2}$ for any direction other than the tangential one. In the latter case $δf$ shows a discontinuity in the third derivative.