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 δv = kδh, 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 ∼ const(δh)3/2 for any direction other than the tangential one. In the latter case δf shows a discontinuity in the third derivative. PACS numbers: 05.50, 64.60C, 64.70R